A farmer can lease land up to maximum of 1000 acres. He has to pay $5 per
acre per year if he leases up to 600 acres. Beyond 600 acres, he can lease
at $8 per acre per year. He grows corn on the land. He can grow corn at the
normal level or at an intense level (more fertilizer,
frequent irrigation, etc.) Normal level yields 70 bushels per acre. Intense
level yields 100 bushels per acre. The cultivation requirements are given in
the table at the bottom. Harvesting requires 0.5 man-hours of labor per
bushel harvested. The farmer can sell corn at the rate of $2.50 per bushel
in the wholesale market. He can also raise poultry. Poultry is measured in
poultry units. To raise one poultry unit requires 25 bushels of corn, 20
man-hours of labor, and 25 ft of shed floor space.
He can either use the corn that he has grown himself or buy corn from the
retail market. He gets corn at the rate of $3.50 per unit.
He can sell at the price
of \$175 per poultry unit in the wholesale market up to 200 units. Any
amount of poultry over 200 units sells for \$160 per unit. He has only one
shed for raising poultry with 15,000 ft of floor
space. He and his family can contribute 4000 man-hours of labor per year at
no cost. if he needs more labor, he can hire it at $3 per man-hour up to
3000 man-hours. For any amount of labor hired over 3000 man-hours, he has to
pay $6 per man-hour. Formulate an LP to maximize his net profit.