Question: Formulate the following linear program and solve the resulting formulations. discuss your results.

A farmer has 100 acres which can be used for growing wheat or corn. The yield is 60 bushels per acre per year of wheat or 95 bushels of corn. Any fraction of the 100 acres can be devoted to growing wheat and/or corn. Labor requirements are 4 hours per acre per year, plus .15 hour per bushel of wheat and .70 hour per bushel of corn. Cost of seed, fertilizer, etc. is 40 cents per bushel of wheat and 30 cents per bushel of corn. Wheat can be sold for 3.75 per bushel, and corn for 2.95 per bushel. wheat can be bought for 4.25 per bushel, and corn for 3.50 per bushel.

In addition the farmer may raise pigs and/or poultry. The farmer sells the pigs or poultry when they reach the age of one year. A pig sells for 150$. he measures the poultry in terms of one "pig equivalent" (the number of chickens needed to bring in 150$ at the time of the sale.) One pig requires 25 bushels of wheat or 20 bushels of corn, plus 25 hours of labor and 25 square feet of floor space. an equivalent amount of poultry requires 25 bushels of corn or 10 bushels of wheat, 40 hours of labor, and 15 square feet of floor space. The farmer has 10000 square feet of floor space. he has available per year 2000 hours of his own tiMeand another 2000 hours from his family. He can hire labor at 7.50 per hour. However, for each hour of hired labor, .15 hour of the farmers time is required for supervision. How much land should be devoted to corn and how much to wheat, and in addition, how many pigs and/or poultry should be raised to maximize the

farmers profits?