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Linear Programming : Objective Function and Optimal Solution

Pet Supplies Company produces 16-ounce cans of dog food by combining meat by-products, which cost $0.60 per pound, and chicken by-products, which cost $0.35 per pound. Meat by-products are 55% protein and 30% fat by weight, while chicken by-products are 40% protein and 10% fat by weight. To meet customer expectations, the final product should contain at least 50% protein and between 15 and 25% fat by weight.

a) Formulate a linear programming solution to be used to determine what the composition of the dog food should be to meet the various requirements at the minimum cost.

b) Using linear programming, find the optimal solution for the objective function and the optimal value of the variables.

Solution Preview

(a) We know, one pound is 16 ounces. Suppose the 16-ounce can of dog food is
combined with x pounds of meat by-products and y pounds of chicken by-products.
Then the objective function is z=0.6x+0.35y, which is the cost of the can.
Now we discuss the restrictions of x and y.
1. The weight of the can is 16 ounces or 1 pound. So ...

Solution Summary

An LP pproblem is solved.