Question: Dwight is an elementary school teacher who also raises pigs for supplemental income. He is trying to decide what to feed his pigs. He is considering using a combination of pig feeds available from the local supplier. He would like to feed the pigs at minimum cost while also making sure each pig receives an adequate supply of calories and vitamins. The cost, calorie content, and vitamin content of each feed is given in the table below.

Each pig requires at least 8,000 calories per day and at least 700 units of vitamins. A further constraint is that no more than 1/3 of the diet (by weight) can consist of Feed Type A, since it contains an ingredient that is toxic if consumed in too large a quantity.

a. Identify verbally the decisions to be made, the constraints on these decisions, and the overall measure of performance for the decisions.

b. Convert these verbal descriptions of the constraints and the measure of performance into quantitative expressions in terms of the data and decisions.

E*

c. Formulate and solve a linear programming model for this problem on a spreadsheet.

d. Formulate this same model algebraically.