Problem 2. (14 points) Two products, A and B, are processed on three machines: M1, M2 and M3. The processing times per unit, machine availability, and profit per unit are provided in the table below. Additionally, any unutilized time on machine M3 can be given on a rental basis to another firm at a rate of $1.50 per hour. Processing time (hours) Machine A B Availability (hours) M 2 3 1,500 M2 3 2 1,500 M3 1 1 1,000 Profit $10 $12 1. Set-up the profit maximizing linear programming problem and numerically solve. Problem 1. (28 points) A farmer has 1,000 acres of land in which he can grow corn, wheat or soybeans. Each acre of corn costs $100 for preparation, requires 7 man-days of work, and yields a profit of $30. An acre of wheat costs $120 for preparation, requires 10 man-days of work, and yields a profit of $40. An acre of soybeans costs $70 for preparation, requires 8 man-days of work, and yields a profit of $20. The farmer has $1,000,000 for preparation and 8,000 man-days of work available. How many acres of corn, wheat, and soybeans should be farmed? 1. Set-up the resulting linear programming problem and numerically solve. 2. If the profit per acre of each crop type were to double, would the number of acres farmed of each type change? 3. How sensitive is the solution on the amount of money available for preparation? Would the number of acres farmed of each type change if more money were available? What if less money were available