Model 14: Farm Planning

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 ft2 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 ft2 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.

Requirements per Acre per Year Normal Level Intense Level
Labor (man-hours) 6 9
Materials (seed, fertilizer, water, etc.) $20 $35