9. A sausage company needs to determine how many pounds of premium hot dogs and

Question

9. A sausage company needs to determine how many pounds of premium hot dogs and how many pounds of regular hot dogs it should manufacture, in order to maximize its profit. Each pound of premium hot dogs uses 0.65 lb of beef, 0.15 lb of pork and 0.20 lb of filler for its manufacture. Each pound of regular hot dogs uses 0.25 lb of beef, 0.35 lb of pork and 0.40 lb of filler. Suppliers can provide the company with a maximum of 2000 lb of beef, 1000 lb of pork and 1500 lb of filler. The company needs to produce at least 2000 lb of regular hot dogs to meet contract requirements. The company makes a profit of $0.60 per lb on premium hot dogs and $0.35 per lb on regular hot dogs. Formulate, but DO NOT SOLVE, a linear program, the solution of which would tell the company how many pounds of each variety of hot dog it should make. In your formulation: (1) Clearly specify the variables (2) Give the objective function and specify whether the objective is max or min (3) List all the constraints.

Explanation / Answer

let x = quantity of premium hot dogs

y = quantity of regular hot dogs

setting up the constraints

.65 x + .25y <= 2000

.15x + ..35y <= 1000

.20 x + .40y <= 1500

y >= 2000

objective function is

P = .60x +.35y

the objective function is maximum

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