A feed company produces a livestock mix from four possible ingredients: corn, pe

Question

A feed company produces a livestock mix from four possible ingredients: corn, peanuts, oats, and a vitamin supplement. The company produces the feed mix in 2,000 pound batches. Corn costs $0.10/lb, peanuts $0.05/lb, oats $0.15/lb, and the vitamin supplement $0.20/lb. Customers require the following criteria to be met:
• The mix must contain at least 30% peanuts.
• The mix cannot contain more than 20% oats.
• Each batch must contain at least 10% vitamin supplement.
• The ratio of corn and oats to peanuts must be at least 3 to 2.

What is the optimum batch mix that minimizes total cost?

a) Formulate this problem usinga linear programming model.
b) Solve this model by using graphical analysis.

Explanation / Answer

Let C, P, O and V represent quantity of corn, peanuts, oats, and a vitamin supplement in a batch/mix respectively.

we haeve to maximize profit z.

so, objective function is:-

maximize z = 0.1*C + 0.05*P + 0.15*O + 0.2*V

subect to constraints : P + O + C + V = 2000;

                                   P >= 600;

                                   O <= 400;

                                   V >= 200;

                                   2*C - 3*O >= 0;

                                   O >= 0;

                                   C >= 0.

since there are 4 variables, the formulation cannot be solved graphically.

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