# The Southfork Feed Company makes a feed mix from four ingredientsoats, corn, soybeans, and a vitamin supplement.

## Question:

At least 30% of the mix must be soybeans.

At least 20% of the mix must be the vitamin supplement.

The ratio of corn to oats cannot exceed 2 to 1.

The amount of oats cannot exceed the amount of soybeans.

The mix must be at least 500 pounds.

A pound of oats costs $0.50; a pound of corn, $1.20; a pound of soybeans, $0.60; and a pound of vitamin supplement, $2.00. The feed company wants to know the number of pounds of each ingredient to put in the mix in order to minimize cost.

a. Formulate a linear programming model for this problem.

b. Solve the model by using the computer.

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