Suppose you were interested in a farm family in a developing country that sold part of its harvest each year for needed currency, but mainly relied on the farm to meet its own food needs. The farm grows beans, corn, and lettuce for sale and its own consumption. Suppose the limiting production resources are land and labor, and it is endowed with 10 acres of land and 5,000 hours of family labor. It faces the following per acres resource requirements:
Resource Beans Corn Lettuce
|
Land
|
1
|
1
|
1
|
|
Labor
|
1,000
|
1,300
|
1,400
|
For every acre, the farmer can produce 60 bushels of beans, 80 bushels of corn, and 1,000 head of lettuce. It can receive the following unit profits if the produce is sold on the market: $8 per bushel of beans, $6 per bushel of corn, and $2 per head of lettuce. In addition, the farm-family needs to produce enough to have 50 bushels of beans, 100 bushels of corn, and 365 head of lettuce for their own consumption. Formulate an LP model that maximizes profit from the sale of produce while meeting the constraints outlined in this exercise including the minimum consumption constraints. Solve the exercise using Solver.