A farmer owns 150 acres of land and plans to sow wheat, rice, and corn. He can use the storage facility of the government but must reserve the space before planting crops. He receives water free from the public canal. For planning purposes, the farmer must mention his plantation area to the public authority. He expects that the yield per acre of wheat will be 15 tons, yield per acre of rice will be 18 tons, and yield per acre of corn will be 20 tons. He can reserve up to 3,000 tons of public storage space to stock his produce. The farmer employs 2,000 laborers. An acre of wheat plantation requires 12 laborers, an acre of rice plantation requires 10 laborers, and an acre of corn plantation requires 18 laborers. The farmer wants to determine the number of acres to plant each type of produce to maximize his yield.
a. Formulate an integer programming model for this problem.
b. Solve this model by using the computer.