4x² ( 8x² - 7xy + 3y²) =
2 answers:
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Answer:
a) Objective function (minimize cost):
Restrictions
Proteins per pound:
Vitamins per pound:
Non-negative values:
b) Attached
c) The optimum solution (minimum cost) is 0 pounds of ingredient A and 0.75 pounds of ingredient B. The cost is $0.15 per ration.
d) The optimum solution changes. The cost is now 0 pounds of ingredient A and 0.625 pounds of ingredient B. The cost is $0.125 per ration.
Step-by-step explanation:
a) The LP formulation for this problem is:
Objective function (minimize cost):
Restrictions
Proteins per pound:
Vitamins per pound:
Non-negative values:
b) The feasible region is attached.
c) We have 3 corner points. In one of them lies the optimal solution.
Corner A=0 B=0.75
Corner A=0.5 B=0.5
Corner A=0.75 B=0
The optimum solution (minimum cost) is 0 pounds of ingredient A and 0.75 pounds of ingredient B. The cost is $0.15 per ration.
d) If the company requires only 5 units of vitamins per pound rather than 6, one of the restrictions change.
The feasible region changes two of its three corners:
Corner A=0 B=0.625
Corner A=0.583 B=0.333
Corner A=0.75 B=0
The optimum solution changes. The cost is now 0 pounds of ingredient A and 0.625 pounds of ingredient B. The cost is $0.125 per ration.
