GRAPHCAL SENSTVTY ANALYSS

2. A production facility manufactures two types of products using both machine and labor resources. Product 1 requires 2 machine-hours and 1 man-hour, while product 2 requires 3 machine-hours and 1 man-hour. Each product 1 sells for \$5, product 2 sells for \$7. All products manufactured can be sold. At present, the production facility has 19 machine-hours and 8 manhours per day. The market limit for product 1 is 6 units per day. To maximize the profit, the production facility should solve the following LP: x1 : number of units of product 1 produced daily, x2 : number of units of product 2 produced daily. Maxz=5x1+7x2s.t.x162x1+3x219x1+x28x1,x20 a. Solve the LP graphically. b. Suppose that the profit of product 2 is changed to $6. Would the optimal solution change? If yes, find the new optimal solution. If not, explain why and find the new profit. c. Suppose that the market limit for product 1 changes to 7 units per day. What would the profit now be? Explain why. d. What is the most that the production facility would be willing to pay for another machine-hour? If 22 machine-hours are available, what would be the new profit value