Q&A Hero

Q: If a system depends on two subsystems functioning when activated, the reliability of that system is equal to that of the less reliable subsystem.

Q: Reliability is the probability that a product or system will function when activated.

Q: A company produces two products (A and B) using three resources (I, II, and III). Each product A requires 1 unit of resource I and 3 units of resource II and has a profit of $1. Each product B requires 2 units of resource I, 3 units of resource II, and 4 units of resource III and has a profit of $3. Resource I is constrained to 40 units maximum per day; resource II, 90 units; and resource III, 60 units. What is the slack (unused amount) for each resource for the optimum production combination?

Q: A company produces two products (A and B) using three resources (I, II, and III). Each product A requires 1 unit of resource I and 3 units of resource II and has a profit of $1. Each product B requires 2 units of resource I, 3 units of resource II, and 4 units of resource III and has a profit of $3. Resource I is constrained to 40 units maximum per day; resource II, 90 units; and resource III, 60 units. What is the optimum production combination and its profits?

Q: A company produces two products (A and B) using three resources (I, II, and III). Each product A requires 1 unit of resource I and 3 units of resource II and has a profit of $1. Each product B requires 2 units of resource I, 3 units of resource II, and 4 units of resource III and has a profit of $3. Resource I is constrained to 40 units maximum per day; resource II, 90 units; and resource III, 60 units. Is the production combination 15 A's and 15 B's feasible?

Q: A company produces two products (A and B) using three resources (I, II, and III). Each product A requires 1 unit of resource I and 3 units of resource II and has a profit of $1. Each product B requires 2 units of resource I, 3 units of resource II, and 4 units of resource III and has a profit of $3. Resource I is constrained to 40 units maximum per day; resource II, 90 units; and resource III, 60 units. Is the production combination 10 A's and 10 B's feasible?

Q: A company produces two products (A and B) using three resources (I, II, and III). Each product A requires 1 unit of resource I and 3 units of resource II and has a profit of $1. Each product B requires 2 units of resource I, 3 units of resource II, and 4 units of resource III and has a profit of $3. Resource I is constrained to 40 units maximum per day; resource II, 90 units; and resource III, 60 units. What are the corner points of the feasible solution space?

Q: A company produces two products (A and B) using three resources (I, II, and III). Each product A requires 1 unit of resource I and 3 units of resource II and has a profit of $1. Each product B requires 2 units of resource I, 3 units of resource II, and 4 units of resource III and has a profit of $3. Resource I is constrained to 40 units maximum per day; resource II, 90 units; and resource III, 60 units. What is the objective function?

Q: Wood Specialties Company produces wall shelves, bookends, and shadow boxes. It is necessary to plan the production schedule for next week. The wall shelves, bookends, and shadow boxes are made of oak, of which the company has 600 board feet. A wall shelf requires 4 board feet, bookends require 2 board feet, and a shadow box requires 3 board feet. The company has a power saw for cutting the oak boards into the appropriate pieces; a wall shelf requires 30 minutes, bookends require 15 minutes, and a shadow box requires 15 minutes. The power saw is expected to be available for 36 hours next week. After cutting, the pieces of work in process are hand finished in the finishing department, which consists of 4 skilled and experienced craftsmen, each of whom can complete any of the products. A wall shelf requires 60 minutes of finishing, bookends require 30 minutes, and a shadow box requires 90 minutes. The finishing department is expected to operate for 40 hours next week. Wall shelves sell for $29.95 and have a unit variable cost of $17.95; bookends sell for $11.95 and have a unit variable cost of $4.95; a shadow box sells for $16.95 and has a unit variable cost of $8.95. (A) Is this a problem in maximization or minimization? (B) What are the decision variables? Suggest symbols for them. (C) What is the objective function? (D) What are the constraints?

Q: A small firm makes three products, which all follow the same three-step process, which consists of milling, inspection, and drilling. Product A requires 6 minutes of milling, 5 minutes of inspection, and 4 minutes of drilling; product B requires 2.5 minutes of milling, 2 minutes of inspection, and 2 minutes of drilling; and product C requires 5 minutes of milling, 4 minutes of inspection, and 8 minutes of drilling. The department has 20 hours available during the next period for milling, 15 hours for inspection, and 24 hours for drilling. Product A contributes $6.00 per unit to profit, product B contributes $4.00 per unit, and product C contributes $10.00 per unit. Use the following computer output to find the optimum mix of products in terms of maximizing contributions to profits for the next period.

Q: Consider the following linear programming problem: Determine the optimum amounts of x and y in terms of cost minimization. What is the minimum cost?

Q: Solve the following linear programming problem:

Q: Given this problem: (A) Solve for the quantities of x and y which will maximize Z. (B) What is the maximum value of Z?

Q: A manager must decide on the mix of products to produce for the coming week. Product A requires three minutes per unit for molding, two minutes per unit for painting, and one minute per unit for packing. Product B requires two minutes per unit for molding, four minutes per unit for painting, and three minutes per unit for packing. There will be 600 minutes available for molding, 600 minutes for painting, and 420 minutes for packing. Both products have profits of $1.50 per unit. (A) What combination of A and B will maximize profit? (B) What is the maximum possible profit? (C) How much of each resource will be unused for your solution?

Q: Consider the following linear programming problem: Solve the values of x and y that will maximize revenue. What revenue will result?

Q: It has been determined that, with respect to resource X, a one-unit increase in availability of X would lead to a $3.50 increase in the value of the objective function. This value would be X's: A. range of optimality. B. shadow price. C. range of feasibility. D. slack. E. surplus.

Q: _________________ is a means of assessing the impact of changing parameters in a linear programming model. A. Simulplex B. Simplex C. Slack D. Surplus E. Sensitivity

Q: Once we go beyond two decision variables, typically the ___________ method of linear programming must be used. A. simplicit B. unidimensional C. simplex D. dynamic E. exponential

Q: When we use less of a resource than was available, in linear programming that resource would be called non-__________. A. binding B. feasible C. reduced cost D. linear E. enumerated

Q: A novice linear programmer is dealing with a three-decision-variable problem. To compare the attractiveness of various feasible decision-variable combinations, values of the objective function at corners are calculated. This is an example of: A. empiritation. B. explicitation. C. evaluation. D. enumeration. E. elicitation.

Q: The logistics/operations manager of a mail order house purchases two products for resale: king beds (K) and queen beds (Q). Each king bed costs $500 and requires 100 cubic feet of storage space, and each queen bed costs $300 and requires 90 cubic feet of storage space. The manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. Profit for each king bed is $300 and for each queen bed is $150. For the purchase combination 0 king beds and 200 queen beds, which resource is slack (not fully used)? A. investment money (only) B. storage space (only) C. both investment money and storage space D. neither investment money nor storage space E. cannot be determined exactly

Q: The logistics/operations manager of a mail order house purchases two products for resale: king beds (K) and queen beds (Q). Each king bed costs $500 and requires 100 cubic feet of storage space, and each queen bed costs $300 and requires 90 cubic feet of storage space. The manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. Profit for each king bed is $300 and for each queen bed is $150. What is the maximum profit? A. $0 B. $30,000 C. $42,000 D. $45,000 E. $54,000

Q: The logistics/operations manager of a mail order house purchases two products for resale: king beds (K) and queen beds (Q). Each king bed costs $500 and requires 100 cubic feet of storage space, and each queen bed costs $300 and requires 90 cubic feet of storage space. The manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. Profit for each king bed is $300 and for each queen bed is $150. Which of the following is not a feasible purchase combination? A. 0 king beds and 0 queen beds B. 0 king beds and 250 queen beds C. 150 king beds and 0 queen beds D. 90 king beds and 100 queen beds E. 0 king beds and 200 queen beds

Q: The logistics/operations manager of a mail order house purchases two products for resale: king beds (K) and queen beds (Q). Each king bed costs $500 and requires 100 cubic feet of storage space, and each queen bed costs $300 and requires 90 cubic feet of storage space. The manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. Profit for each king bed is $300 and for each queen bed is $150. What is the storage space constraint? A. 200K + 100Q ≤ 18,000 B. 200K + 90Q ≤ 18,000 C. 300K + 90Q ≤ 18,000 D. 500K + 100Q ≤ 18,000 E. 100K + 90Q ≤ 18,000

Q: The logistics/operations manager of a mail order house purchases two products for resale: king beds (K) and queen beds (Q). Each king bed costs $500 and requires 100 cubic feet of storage space, and each queen bed costs $300 and requires 90 cubic feet of storage space. The manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. Profit for each king bed is $300 and for each queen bed is $150. What is the objective function? A. Z = $150K + $300Q B. Z = $500K + $300Q C. Z = $300K + $150Q D. Z = $300K + $500Q E. Z = $100K + $90Q

Q: The owner of Crackers, Inc., produces two kinds of crackers: Deluxe (D) and Classic (C). She has a limited amount of the three ingredients used to produce these crackers available for her next production run: 4,800 ounces of sugar; 9,600 ounces of flour, and 2,000 ounces of salt. A box of Deluxe crackers requires 2 ounces of sugar, 6 ounces of flour, and 1 ounce of salt to produce; while a box of Classic crackers requires 3 ounces of sugar, 8 ounces of flour, and 2 ounces of salt. Profits for a box of Deluxe crackers are $.40; and for a box of Classic crackers, $.50. For the production combination of 800 boxes of Deluxe and 600 boxes of Classic, which resource is slack (not fully used)? A. sugar (only) B. flour (only) C. salt (only) D. sugar and flour E. sugar and salt

Q: The owner of Crackers, Inc., produces two kinds of crackers: Deluxe (D) and Classic (C). She has a limited amount of the three ingredients used to produce these crackers available for her next production run: 4,800 ounces of sugar; 9,600 ounces of flour, and 2,000 ounces of salt. A box of Deluxe crackers requires 2 ounces of sugar, 6 ounces of flour, and 1 ounce of salt to produce; while a box of Classic crackers requires 3 ounces of sugar, 8 ounces of flour, and 2 ounces of salt. Profits for a box of Deluxe crackers are $.40; and for a box of Classic crackers, $.50. What are profits for the optimal production combination? A. $800 B. $500 C. $640 D. $620 E. $600

Q: The owner of Crackers, Inc., produces two kinds of crackers: Deluxe (D) and Classic (C). She has a limited amount of the three ingredients used to produce these crackers available for her next production run: 4,800 ounces of sugar; 9,600 ounces of flour, and 2,000 ounces of salt. A box of Deluxe crackers requires 2 ounces of sugar, 6 ounces of flour, and 1 ounce of salt to produce; while a box of Classic crackers requires 3 ounces of sugar, 8 ounces of flour, and 2 ounces of salt. Profits for a box of Deluxe crackers are $.40; and for a box of Classic crackers, $.50. Which of the following is not a feasible production combination? A. 0 D and 0 C B. 0 D and 1,000 C C. 800 D and 600 C D. 1,600 D and 0 C E. 0 D and 1,200 C

Q: The owner of Crackers, Inc., produces two kinds of crackers: Deluxe (D) and Classic (C). She has a limited amount of the three ingredients used to produce these crackers available for her next production run: 4,800 ounces of sugar; 9,600 ounces of flour, and 2,000 ounces of salt. A box of Deluxe crackers requires 2 ounces of sugar, 6 ounces of flour, and 1 ounce of salt to produce; while a box of Classic crackers requires 3 ounces of sugar, 8 ounces of flour, and 2 ounces of salt. Profits for a box of Deluxe crackers are $.40; and for a box of Classic crackers, $.50. What is the constraint for sugar? A. 2D + 3C ≤ 4,800 B. 6D + 8C ≤ 4,800 C. 1D + 2C ≤ 4,800 D. 3D + 2C ≤ 4,800 E. 4D + 5C ≤ 4,800

Q: The owner of Crackers, Inc., produces two kinds of crackers: Deluxe (D) and Classic (C). She has a limited amount of the three ingredients used to produce these crackers available for her next production run: 4,800 ounces of sugar; 9,600 ounces of flour, and 2,000 ounces of salt. A box of Deluxe crackers requires 2 ounces of sugar, 6 ounces of flour, and 1 ounce of salt to produce; while a box of Classic crackers requires 3 ounces of sugar, 8 ounces of flour, and 2 ounces of salt. Profits for a box of Deluxe crackers are $.40; and for a box of Classic crackers, $.50. What is the objective function? A. $.50D + $.40C = Z B. $.20D + $.30C = Z C. $.40D + $.50C = Z D. $.10D + $.20C = Z E. $.60D + $.80C = Z

Q: A local bagel shop produces two products: bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's production run. Bagel profits are 20 cents each, and croissant profits are 30 cents each. For the production combination of 600 bagels and 800 croissants, which resource is slack (not fully used)? A. flour (only) B. sugar (only) C. flour and yeast D. flour and sugar E. yeast and sugar

Q: A local bagel shop produces two products: bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's production run. Bagel profits are 20 cents each, and croissant profits are 30 cents each. What are optimal profits for today's production run? A. $580 B. $340 C. $220 D. $380 E. $420

Q: A local bagel shop produces two products: bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's production run. Bagel profits are 20 cents each, and croissant profits are 30 cents each. Which of the following is not a feasible production combination? A. 0 B and 0 C B. 0 B and 1,100 C C. 800 B and 600 C D. 1,100 B and 0 C E. 0 B and 1,400 C

Q: A local bagel shop produces two products: bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's production run. Bagel profits are 20 cents each, and croissant profits are 30 cents each. What is the sugar constraint (in tablespoons)? A. 6B + 3C ≤ 4,800 B. 1B + 1C ≤ 4,800 C. 2B + 4C ≤ 4,800 D. 4B + 2C ≤ 4,800 E. 2B + 3C ≤ 4,800

Q: A local bagel shop produces two products: bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's production run. Bagel profits are 20 cents each, and croissant profits are 30 cents each. What is the objective function? A. $0.30B + $0.20C = Z B. $0.60B + $0.30C = Z C. $0.20B + $0.30C = Z D. $0.20B + $0.40C = Z E. $0.10B + $0.10C = Z

Q: An electronics firm produces two models of pocket calculators: the A-100 (A), which is an inexpensive four-function calculator, and the B-200 (B), which also features square root and percent functions. Each model uses one (the same) circuit board, of which there are only 2,500 available for this week's production. Also, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators, of which the A-100 requires 15 minutes (.25 hours) each, and the B-200 requires 30 minutes (.5 hours) each to produce. The firm forecasts that it could sell a maximum of 4,000 A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each, and profits for the B-200 are $4.00 each. For the production combination of 1,400 A-100s and 900 B-200s, which resource is slack (not fully used)? A. circuit boards (only) B. assembly time (only) C. both circuit boards and assembly time D. neither circuit boards nor assembly time E. cannot be determined exactly

Q: An electronics firm produces two models of pocket calculators: the A-100 (A), which is an inexpensive four-function calculator, and the B-200 (B), which also features square root and percent functions. Each model uses one (the same) circuit board, of which there are only 2,500 available for this week's production. Also, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators, of which the A-100 requires 15 minutes (.25 hours) each, and the B-200 requires 30 minutes (.5 hours) each to produce. The firm forecasts that it could sell a maximum of 4,000 A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each, and profits for the B-200 are $4.00 each. What are optimal weekly profits? A. $10,000 B. $4,600 C. $2,500 D. $5,200 E. $6,400

Q: An electronics firm produces two models of pocket calculators: the A-100 (A), which is an inexpensive four-function calculator, and the B-200 (B), which also features square root and percent functions. Each model uses one (the same) circuit board, of which there are only 2,500 available for this week's production. Also, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators, of which the A-100 requires 15 minutes (.25 hours) each, and the B-200 requires 30 minutes (.5 hours) each to produce. The firm forecasts that it could sell a maximum of 4,000 A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each, and profits for the B-200 are $4.00 each. Which of the following is not a feasible production/sales combination? A. 0 A and 0 B B. 0 A and 1,000 B C. 1,800 A and 700 B D. 2,500 A and 0 B E. 100 A and 1,600 B

Q: An electronics firm produces two models of pocket calculators: the A-100 (A), which is an inexpensive four-function calculator, and the B-200 (B), which also features square root and percent functions. Each model uses one (the same) circuit board, of which there are only 2,500 available for this week's production. Also, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators, of which the A-100 requires 15 minutes (.25 hours) each, and the B-200 requires 30 minutes (.5 hours) each to produce. The firm forecasts that it could sell a maximum of 4,000 A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each, and profits for the B-200 are $4.00 each. What is the assembly time constraint (in hours)? A. 1A + 1B ≤ 800 B. .25A + .5B ≤ 800 C. .5A + .25B ≤ 800 D. 1A + .5B ≤ 800 E. .25A + 1B ≤ 800

Q: An electronics firm produces two models of pocket calculators: the A-100 (A), which is an inexpensive four-function calculator, and the B-200 (B), which also features square root and percent functions. Each model uses one (the same) circuit board, of which there are only 2,500 available for this week's production. Also, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators, of which the A-100 requires 15 minutes (.25 hours) each, and the B-200 requires 30 minutes (.5 hours) each to produce. The firm forecasts that it could sell a maximum of 4,000 A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each, and profits for the B-200 are $4.00 each. What is the objective function? A. $4.00A + $1.00B = Z B. $0.25A + $1.00B = Z C. $1.00A + $4.00B = Z D. $1.00A + $1.00B = Z E. $0.25A + $0.50B = Z

Q: The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R) and sassafras soda (S). Two resources are constrained: production time (T), of which she has at most 12 hours per day; and carbonated water (W), of which she can get at most 1,500 gallons per day. A case of root beer requires 2 minutes of time and 5 gallons of water to produce, while a case of sassafras soda requires 3 minutes of time and 5 gallons of water. Profits for the root beer are $6.00 per case, and profits for the sassafras soda are $4.00 per case. For the production combination of 180 root beer and 0 sassafras soda, which resource is slack (not fully used)? A. production time (only) B. carbonated water (only) C. both production time and carbonated water D. neither production time nor carbonated water E. cannot be determined exactly

Q: The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R) and sassafras soda (S). Two resources are constrained: production time (T), of which she has at most 12 hours per day; and carbonated water (W), of which she can get at most 1,500 gallons per day. A case of root beer requires 2 minutes of time and 5 gallons of water to produce, while a case of sassafras soda requires 3 minutes of time and 5 gallons of water. Profits for the root beer are $6.00 per case, and profits for the sassafras soda are $4.00 per case. What are optimal daily profits? A. $960 B. $1,560 C. $1,800 D. $1,900 E. $2,520

Q: The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R) and sassafras soda (S). Two resources are constrained: production time (T), of which she has at most 12 hours per day; and carbonated water (W), of which she can get at most 1,500 gallons per day. A case of root beer requires 2 minutes of time and 5 gallons of water to produce, while a case of sassafras soda requires 3 minutes of time and 5 gallons of water. Profits for the root beer are $6.00 per case, and profits for the sassafras soda are $4.00 per case. Which of the following is not a feasible production combination? A. 0 R and 0 S B. 0 R and 240 S C. 180 R and 120 S D. 300 R and 0 S E. 180 R and 240 S

Q: The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R) and sassafras soda (S). Two resources are constrained: production time (T), of which she has at most 12 hours per day; and carbonated water (W), of which she can get at most 1,500 gallons per day. A case of root beer requires 2 minutes of time and 5 gallons of water to produce, while a case of sassafras soda requires 3 minutes of time and 5 gallons of water. Profits for the root beer are $6.00 per case, and profits for the sassafras soda are $4.00 per case. What is the production time constraint (in minutes)? A. 2R + 3S ≤ 720 B. 2R + 5S ≤ 720 C. 3R + 2S ≤ 720 D. 3R + 5S ≤ 720 E. 5R + 5S ≤ 720

Q: The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R) and sassafras soda (S). Two resources are constrained: production time (T), of which she has at most 12 hours per day; and carbonated water (W), of which she can get at most 1,500 gallons per day. A case of root beer requires 2 minutes of time and 5 gallons of water to produce, while a case of sassafras soda requires 3 minutes of time and 5 gallons of water. Profits for the root beer are $6.00 per case, and profits for the sassafras soda are $4.00 per case. What is the objective function? A. $4R + $6S = Z B. $2R + $3S = Z C. $6R + $4S = Z D. $3R + $2S = Z E. $5R + $5S = Z

Q: The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). Two of his resources are constrained: production time, which is limited to 8 hours (480 minutes) per day; and malt extract (one of his ingredients), of which he can get only 675 gallons each day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract, while each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg, and profits for Dark beer are $2.00 per keg. For the production combination of 135 Lite and 0 Dark, which resource is slack (not fully used)? A. time (only) B. malt extract (only) C. both time and malt extract D. neither time nor malt extract E. cannot be determined exactly

Q: The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). Two of his resources are constrained: production time, which is limited to 8 hours (480 minutes) per day; and malt extract (one of his ingredients), of which he can get only 675 gallons each day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract, while each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg, and profits for Dark beer are $2.00 per keg. What are optimal daily profits? A. $0 B. $240 C. $420 D. $405 E. $505

Q: The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). Two of his resources are constrained: production time, which is limited to 8 hours (480 minutes) per day; and malt extract (one of his ingredients), of which he can get only 675 gallons each day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract, while each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg, and profits for Dark beer are $2.00 per keg. Which of the following is not a feasible production combination? A. 0 L and 0 D B. 0 L and 120 D C. 90 L and 75 D D. 135 L and 0 D E. 135 L and 120 D

Q: The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). Two of his resources are constrained: production time, which is limited to 8 hours (480 minutes) per day; and malt extract (one of his ingredients), of which he can get only 675 gallons each day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract, while each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg, and profits for Dark beer are $2.00 per keg. What is the time constraint? A. 2L + 3D ≤ 480 B. 2L + 4D ≤ 480 C. 3L + 2D ≤ 480 D. 4L + 2D ≤ 480 E. 5L + 3D ≤ 480

Q: The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). Two of his resources are constrained: production time, which is limited to 8 hours (480 minutes) per day; and malt extract (one of his ingredients), of which he can get only 675 gallons each day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract, while each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg, and profits for Dark beer are $2.00 per keg. What is the objective function? A. $2L + $3D = Z B. $2L + $4D = Z C. $3L + $2D = Z D. $4L + $2D = Z E. $5L + $3D = Z

Q: The production planner for Fine Coffees, Inc., produces two coffee blends: American (A) and British (B). Two of his resources are constrained: Columbia beans, of which he can get at most 300 pounds (4,800 ounces) per week; and Dominican beans, of which he can get at most 200 pounds (3,200 ounces) per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. For the production combination of 0 American and 400 British, which resource is "slack" (not fully used)? A. Colombian beans (only) B. Dominican beans (only) C. both Colombian beans and Dominican beans D. neither Colombian beans nor Dominican beans E. cannot be determined exactly

Q: The production planner for Fine Coffees, Inc., produces two coffee blends: American (A) and British (B). Two of his resources are constrained: Columbia beans, of which he can get at most 300 pounds (4,800 ounces) per week; and Dominican beans, of which he can get at most 200 pounds (3,200 ounces) per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. What are optimal weekly profits? A. $0 B. $400 C. $700 D. $800 E. $900

Q: The production planner for Fine Coffees, Inc., produces two coffee blends: American (A) and British (B). Two of his resources are constrained: Columbia beans, of which he can get at most 300 pounds (4,800 ounces) per week; and Dominican beans, of which he can get at most 200 pounds (3,200 ounces) per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. Which of the following is not a feasible production combination? A. 0 A and 0 B B. 0 A and 400 B C. 200 A and 300 B D. 400 A and 0 B E. 400 A and 400 B

Q: The production planner for Fine Coffees, Inc., produces two coffee blends: American (A) and British (B). Two of his resources are constrained: Columbia beans, of which he can get at most 300 pounds (4,800 ounces) per week; and Dominican beans, of which he can get at most 200 pounds (3,200 ounces) per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. What is the Dominican bean constraint? A. 12A + 8B ≤ 4,800 B. 8A + 12B ≤ 4,800 C. 4A + 8B ≤ 3,200 D. 8A + 4B ≤ 3,200 E. 4A + 8B ≤ 4,800

Q: The production planner for Fine Coffees, Inc., produces two coffee blends: American (A) and British (B). Two of his resources are constrained: Columbia beans, of which he can get at most 300 pounds (4,800 ounces) per week; and Dominican beans, of which he can get at most 200 pounds (3,200 ounces) per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. What is the Columbia bean constraint? A. 1A + 2B ≤ 4,800 B. 12A + 8B ≤ 4,800 C. 2A + 1B ≤ 4,800 D. 8A + 12B ≤ 4,800 E. 4A + 8B ≤ 4,800

Q: The production planner for Fine Coffees, Inc., produces two coffee blends: American (A) and British (B). Two of his resources are constrained: Columbia beans, of which he can get at most 300 pounds (4,800 ounces) per week; and Dominican beans, of which he can get at most 200 pounds (3,200 ounces) per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. What is the objective function? A. $1A + $2B = Z B. $12A + $8B = Z C. $2A + $1B = Z D. $8A + $12B = Z E. $4A + $8B = Z

Q: A redundant constraint is one that: A. is parallel to the objective function. B. has no coefficient for at least one decision variable. C. has a zero coefficient for at least one decision variable. D. has multiple coefficients for at least one decision variable. E. does not form a unique boundary of the feasible solution space.

Q: In the graphical approach to linear programming, finding values for the decision variables at the intersection of corners requires the solving of: A. linear constraints. B. surplus variables. C. slack variables. D. simultaneous equations. E. binding constraints.

Q: In a linear programming problem involving maximization, at least one constraint must be of the __________ type. A. greater than or equal B. integer C. binary D. less than or equal E. surplus

Q: In a linear programming problem involving minimization, at least one constraint must be of the __________ type. A. less than or equal B. integer C. greater than or equal D. binary E. slack

Q: An analyst, having solved a linear programming problem, determined that he had 10 more units of resource Q than previously believed. Upon modifying his program, he observed that the optimal solution did not change, but the value of the objective function increased by $30. This means that resource's Q's shadow price was: A. $1.50. B. $3.00. C. $6.00. D. $15.00. E. $30.00.

Q: In a linear programming problem, the objective function was specified as follows: Z = 2A + 4B + 3C The optimal solution calls for A to equal 4, B to equal 6, and C to equal 3. It has also been determined that the coefficient associated with A can range from 1.75 to 2.25 without the optimal solution changing. This range is called A's: A. range of optimality. B. range of feasibility. C. shadow price. D. slack. E. surplus.

Q: In linear programming, sensitivity analysis is associated with: (I) the objective function coefficient. (II) right-hand-side values of constraints. (III) the constraint coefficient. A. I and II only B. II and III only C. I, II, and III D. I and III only E. I only

Q: A constraint that does not form a unique boundary of the feasible solution space is a: A. redundant constraint. B. binding constraint. C. nonbinding constraint. D. feasible solution constraint. E. constraint that equals zero.

Q: In linear programming, a nonzero reduced cost is associated with a: A. decision variable in the solution. B. decision variable not in the solution. C. constraint for which there is slack. D. constraint for which there is surplus. E. constraint for which there is no slack or surplus.

Q: A shadow price reflects which of the following in a maximization problem? A. marginal cost of adding additional resources B. marginal gain in the objective that would be realized by adding one unit of a resource C. net gain in the objective that would be realized by adding one unit of a resource D. marginal gain in the objective that would be realized by subtracting one unit of a resource E. expected value of perfect information

Q: The theoretical limit on the number of constraints that can be handled by the simplex method in a single problem is: A. 1. B. 2. C. 3. D. 4. E. unlimited.

Q: The theoretical limit on the number of decision variables that can be handled by the simplex method in a single problem is: A. 1. B. 2. C. 3. D. 4. E. unlimited.

Q: What combination of x and y will provide a minimum for this problem? A. x = 0, y = 0 B. x = 0, y = 3 C. x = 0, y = 5 D. x = 1, y = 2.5 E. x = 6, y = 0

Q: For the constraints given below, which point is in the feasible solution space of this minimization problem? A. x = .5, y = 5 B. x = 0, y = 4 C. x = 2, y = 5 D. x = 1, y = 2 E. x = 2, y = 1

Q: In graphical linear programming, when the objective function is parallel to one of the binding constraints, then: A. the solution is suboptimal. B. multiple optimal solutions exist. C. a single corner point solution exists. D. no feasible solution exists. E. the constraint must be changed or eliminated.

Q: What combination of x and y will yield the optimum for this problem? A. x = 2, y = 0 B. x = 0, y = 0 C. x = 0, y = 3 D. x = 1, y = 5 E. x = 0, y = 4

Q: Which of the following choices constitutes a simultaneous solution to these equations? A. x = 1, y = 1.5 B. x = .5, y = 2 C. x = 0, y = 3 D. x = 2, y = 0 E. x = 0, y = 0

Q: For the following constraints, which point is in the feasible solution space of this maximization problem? A. x = 1, y = 5 B. x = -1, y = 1 C. x = 4, y = 4 D. x = 2, y = 1 E. x = 2, y = 8

Q: 35. Which objective function has the same slope as this one: $4x + $2y = $20? A. $4x + $2y = $10 B. $2x + $4y = $20 C. $2x - $4y = $20 D. $4x - $2y = $20 E. $8x + $8y = $20

Q: The region which satisfies all of the constraints in graphical linear programming is called the: A. optimum solution space. B. region of optimality. C. lower left hand quadrant. D. region of non-negativity. E. feasible solution space.

Q: The logical approach, from beginning to end, for assembling a linear programming model begins with: A. identifying the decision variables. B. identifying the objective function. C. specifying the objective function parameters. D. identifying the constraints. E. specifying the constraint parameters.

Q: For the products A, B, C, and D, which of the following could be a linear programming objective function? A. Z = 1A + 2B + 3C + 4D B. Z = 1A + 2BC + 3D C. Z = 1A + 2AB + 3ABC + 4ABCD D. Z = 1A + 2B/C + 3D E. Z = 1A + 2B - 1CD

Q: Which of the following could not be a linear programming problem constraint? A. 1A + 2B ≤ 3 B. 1A + 2B ≥ 3 C. 1A + 2B = 3 D. 1A + 2B + 3C + 4D ≤ 5 E. 1A + 2B

Q: Coordinates of all corner points are substituted into the objective function when we use the approach called: A. least squares. B. regression. C. enumeration. D. graphical linear programming. E. constraint assignment.