A farmer has 3000 acres of land, on which he can grow wheat or graze cattle. Three persons are working on the farm, sharing its profits; together they can work 6000 hours per year. They have a working...

A farmer has 3000 acres of land, on which he can grow wheat or graze cattle. Three persons are working on the farm, sharing its profits; together they can work 6000 hours per year. They have a working capital of $90,000. It is assumed that both wheat growing and cattle raising requires no fixed capital, but a working capital of $4 per acre of wheat and $250 per head of cattle. One head of cattle requires 10 acres of grazing land. The average annual number of hours worked per acre of wheat planted is 3V3 hours and per head of cattle is 13’/3 hours. The average net revenue of wheat is $15 per acre and growing $125 per head of cattle.

Solve by means of direct minimization of labor with the constraint that profit should be at least $36,000.