Problem:
Linear Programming, Simplex method - A farmer grows three crops: corn, oats, and soybeans.
"A farmer grows three crops: corn, oats, and soybeans. He mixes these together to feed his own cows and pigs. At least 40% 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 1000 bushels of corn, 500 bushels of oats, and 1000 bushels of soybeans. He needs 1000 bushels of each kind of feed mix for his livestock. The unused corn, oats, and soybeans can be sold for $4, $3.50 and $3.25 a bushels, respectively (and 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 type of feed mix in order to produce sufficient food for the livestock at minimal cost?