A farmer has 500 acres of land and wishes to determine the acreage allocated to the following three crops: wheat, corn, and soybeans. Suppose there are 5,000 man-days available and $60,000 for preparation. The man-days, preparation cost, and profit per acre of the three crops are given below: (a) Determine the linear program, its optimal solution, and the optimal tableau. Solve the linear program by hand, or use a computer to solve the problem and construct the tableau from the optimal solution. (b) Assuming an 8-hour work day, would it be profitable to the farmer to acquire additional help at $3 per hour? Why or why not? (c) Suppose that the farmer has contracted to deliver at least the equivalent of 100 acres of wheat. Use sensitivity analysis to find the new optimal solution. A farmer has 500 acres of land and wishes to determine the acreage allocated to the following three crops: wheat, corn, and soybeans. Suppose there are 5,000 man-days available and $60,000 for preparation. The man-days, preparation cost, and profit per acre of the three crops are given below: (a) Determine the linear program, its optimal solution, and the optimal tableau. Solve the linear program by hand, or use a computer to solve the problem and construct the tableau from the optimal solution. (b) Assuming an 8-hour work day, would it be profitable to the farmer to acquire additional help at $3 per hour? Why or why not? (c) Suppose that the farmer has contracted to deliver at least the equivalent of 100 acres of wheat. Use sensitivity analysis to find the new optimal solution