The Southfork Feed Company makes a feed mix from four ingredients—oats, corn, soybeans, and a vitamin supplement. The company has 300 pounds of oats, 400 pounds of corn, 200 pounds of soybeans, and 100 pounds of vitamin supplement available for the mix. The company has the following requirements for the mix:
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.