Q&A Hero

Question

A craftsman builds two kinds of birdhouses, one for wrens (X1), and one for bluebirds (X2). Each wren birdhouse takes four hours of labor and four units of lumber. Each bluebird house requires two hours of labor and twelve units of lumber. The craftsman has available 60 hours of labor and 120 units of lumber. Wren houses profit $6 each and bluebird houses profit $15 each.

Use the software output that follows to interpret the problem solution. Include a statement of the solution quantities (how many of which product), a statement of the maximum profit achieved by your product mix, and a statement of "resources unused" and "shadow prices."

Answer: The optimal solution is X1 = 12, X2 = 6, which earns a profit of 12 * 6 + 6 * 15 = $162. Both labor and lumber are used up, so there are no resources unused. Additional labor is worth $0.30 per hour, and additional lumber is worth $1.20 per unit.

11) The objective of a linear programming problem is to maximize 1.50A + 1.50B, subject to 3A + 2B u2264 600, 2A + 4B u2264 600, and 1A + 3B u2264 420.

a. Plot the constraints on the grid below

c. Identify the feasible region and its corner points. Show your work.

d. What is the optimal product mix for this problem?

Answer: The objective of the problem is to maximize 1.50A + 1.50B,

The constraints are 3A + 2B u2264 600, 2A + 4B u2264 600, and 1A + 3B u2264 420. The plot and feasible region appear in the graph below. The corner points are (0, 0), (200, 0), (0, 140), and (150, 75). The first three points can be read from the graph axes. The last corner point is the intersection of the equality 2A + 4B = 600 and 3A + 2B = 600. Multiply the first equality by and subtract from the second, leaving 2A = 300 or A = 150. Substituting A = 150 in either equality yields B = 75, which is the optimal product mix for 337.50.

Answer

This answer is hidden. It contains 0 characters.

Related questions

Q: Identify JIT scheduling tactics.
Q: What is a kanban?
Q: What three things does the Toyota Production System (TPS) emphasize?
Q: __________ is any deviation from the optimum process that delivers perfect product on time, every time.
Q: The __________ is the lowest level of quality that we are willing to accept.
Q: The term __________ is used to describe how well a process makes units within design specifications (or tolerances).
Q: The __________ are calculated to show how much allowance should be made for natural variation.
Q: The __________ is a quality control chart that indicates when changes occur in the central tendency of a production process.
Q: Which of the following is true regarding the average outgoing quality level?A) An AOQ value of 1 is ideal, because all defects have been removed.B) AOQ is always greater than AQL but less than LTPD.C) AOQ rises (worsens) following inspection of failed lots.D) AOQ is very low (very good) for extremely poor quality lots.E) None of the above is true.
Q: In most acceptance sampling plans, when a lot is rejected, the entire lot is inspected and all defective items are replaced. When using this technique the AOQA) worsens (AOQ becomes a larger fraction)B) improves (AOQ becomes a smaller fraction)C) is not affected, but the AQL is improvedD) is not affectedE) falls to zero
Q: A Type II error occurs whenA) a good lot is rejectedB) a bad lot is acceptedC) the population is worse than the LTPDD) the proportion of defectives is very smallE) none of the above
Q: Average outgoing quality (AOQ) usuallyA) worsens with inspectionB) stays the same with inspectionC) improves with inspectionD) may either improve or worsen with inspectionE) is the average quality before inspectionAnswer: C
Q: Which of the following is true regarding the relationship between AOQ and the true population percent defective?A) AOQ is greater than the true percent defective.B) AOQ is the same as the true percent defective.C) AOQ is less than the true percent defective.D) There is no relationship between AOQ and the true percent defective.E) The relationship between these two cannot be determined.
Q: Acceptance samplingA) may involve inspectors taking random samples (or batches) of finished products and measuring them against predetermined standardsB) may involve inspectors taking random samples (or batches) of incoming raw materials and measuring them against predetermined standardsC) is more economical than 100% inspectionD) may be either of a variable or attribute type, although attribute inspection is more common in the business environmentE) All of the above are true.
Q: A Cp of 1.33 indicates how many sigma limitsA) 1B) 1.33C) 2D) 3E) 4
Q: The normal application of a p-chart is inA) process sampling by variablesB) acceptance sampling by variablesC) process sampling by attributesD) acceptance sampling by attributesE) none of the above
Q: The mean and standard deviation for a process for which we have a substantial history are= 120 and u03c3 = 2. For the x-bar chart, a sample size of 16 will be used. What is the mean of the sampling distribution?A) 1/8 (0.125)B) 7.5C) 2D) 40E) 120
Q: The type of inspection that classifies items as being either good or defective isA) variable inspectionB) attribute inspectionC) fixed inspectionD) all of the aboveE) none of the above
Q: Up to three standard deviations above or below the centerline is the amount of variation that statistical process control allows forA) Type I errorsB) about 95.5% variationC) natural variationD) all types of variationE) assignable variation
Q: Suppose that a three stage process had reliability ratings of .7, .8, and .9 at each station and that a failure at any station represented a failure for the entire process. If each station is given a redundant check with .9 reliability, what is the increase in system reliability?
Q: Which product design below has the higher system reliability?
Q: The academic service commonly referred to as "registration" consists of several smaller components: advising, registration for courses, fee assessment, financial aid calculations, and fee payment. Each of these modules operates independently and has some probability of failure for each student. If the five probabilities which accompany these services are 95%, 90%, 99%, 98%, and 99%, what is the "reliability" of the entire product from the student's perspectivethe probability that all five will work according to plan?
Q: Mean charts and range charts complement one another, one detecting shifts in process average, the other detecting shifts in process dispersion.
Q: The x-bar chart indicates that a gain or loss of uniformity has occurred in dispersion of a production process.
Q: A woodworker is concerned about the quality of the finished appearance of her work. In sampling units of a split-willow hand-woven basket, she has found the following number of finish defects in ten units sampled: 4, 0, 3, 1, 2, 0, 1, 2, 0, 2.a. Calculate the average number of defects per basketb. If 3-sigma control limits are used, calculate the lower control limit, centerline, and upper control limit.

Subjects

Accounting Anthropology Archaeology Art History Banking Biology & Life Science Business Business Communication Business Development Business Ethics Business Law Chemistry Communication Computer Science Counseling Criminal Law Curriculum & Instruction Design Earth Science Economic Education Engineering Finance History & Theory Humanities Human Resource International Business Investments & Securities Journalism Law Management Marketing Medicine Medicine & Health Science Nursing Philosophy Physic Psychology Real Estate Science Social Science Sociology Special Education Speech Visual Arts