Chapter 6.4, Problem 46E

In Problems 39-47, construct a mathematical model in the form of a linear programming problem. Do not solve.

Mixing feed. A farmer grows three crops: corn, oats, and soybeans. He mixes them to feed his cows and pigs. At least $40\text{\%}$ of the feed mix for the cows must be corn. The feed mix for the pigs must contain at least twice as much soybeans as corn. He has harvested $1,000$ bushels of corn. 500 bushels of oats, and 1,000 bushels of soybeans. He needs $1,000$ bushels of each feed mix for his livestock. The unused corn, oats, and soybeans can be sold for $\text{\$}4,\text{\$}3.50,$ and $\text{\$}3.25$ a bushel, respectively (thus, these amounts also represent the cost of the crops used to feed the livestock). How many bushels of each crop should be used in each feed mix in order to produce sufficient food for the livestock at a minimal cost?