Question

Muller Farms uses at least 800 lb of special feed daily. The special feed is a mixture of corn and soybean meal with the following compositions:

lb per lb of feedstuff
Feedstuff Protein Fiber Cost ($/lb)
Corn .09 .02 .30
Soybean meal .60 .06 .90
The dietary requirements of the special feed are at least 30% protein and at most 5% fiber. The goal is to determine the daily minimum-cost feed mix.
(a) Formulate a linear programming (LP) problem to model the situation (minimizing cost and satisfying constraints). (Hint: let x1 be the lb of corn in the daily mix, and x2 represent the lb of soybean meal in the daily mix. Formulate objective function and constraints (3 constraints and non-negativity) according to the information given above)
(b) Set up an Excel sheet with the information of this LP problem.
(c) Use Excel Solver to compute the solution to this diet problem.
(d) Include in your report a screenshot of the Excel sheet you used to and a solution.

Answer 1

470.59x₁ + 329,41x₂ = $437.65

Explanation:

minimize: 0.30x₁ + 0.90x₂

where:

x₁ = pounds of corn

x₂ = pounds of soybean

constraints:

x₁ + x₂ ≥ 800

0.09x₁ + 0.60x₂ ≥ 0.30(800) ⇒ 0.09x₁ + 0.60x₂ ≥ 240

0.02x₁ + 0.06x₂ ≤ 0.05(800) ⇒ 0.02x₁ + 0.06x₂ ≤ 40

x₁ ≥ 0

x₂ ≥ 0

the optimal solution is: 470.59x₁ + 329,41x₂ = $437.65