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Question

A feedlot is trying to decide on the lowest cost mix that will still provide adequate nutrition for its cattle. Suppose that the numbers in the chart represent the number of grams of ingredient per 100 grams of feed and that the cost of Feed X is $5/100grams, Feed Y is $3/100grams, and Feed X is $8/100 grams. Each cow will need 50 grams of A per day, 20 grams of B, 30 grams of C, and 10 grams of D. If the feedlot can get no more than 200 grams per day per cow of any of the feed types determine the constraints governing the problem.


Ingredient X Y Z
A 10 15 5
B 30 10 20
C 40 0 20
D 0 20 30

Answer: Objective: Minimize cost = 5X+3Y+8Z where X,Y,Z are in grams and cost is in cents

Subject to:

A requirement: .1X+.15Y+.05Z u2265 50

B requirement: .3X + .1Y + .2Z u2265 20

C requirement: .4X + .2Z u2265 30

D requirement: .2Y+.3Z u226510

Purchase limit: Xu2264200

Purchase limit: Yu2264200

Purchase limit: Zu2264200

Where X,Y, and Z are in grams

22) Suppose that a constraint is given by X+Yu226410. If another constraint is given to be 3X+2Yu226515 determine the corners of the feasible solution. If the profit from X is 5 and the profit from Y is 10, determine the maximum profit.

Answer: Corners are (10,0), (5,0), (0,7.5), and (0,10). Maximum profit is at the corner (0,10), which yields $100 of profit.

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