A firm produces tractors and lawn mowers and make a profit of $30 on each tractors and $30 on each lawn mower. And they sell all they can produce. The time requirement in the machine shop, fabrication, and tractor assembly as well as the maximum time available for each process are given below. Machine Shop Fabrication Assembly Tractor 2 hours 2 hours 1 hour Lawn Mower 1 hour 3 hours 0 hour Hrs. Available 60 hours 120 hours 45 hours a) Formulate a linear program to maximize the profit. Clearly define your decision variables, constraints and objective function b) Solve the formulated linear graphically and find the optimal solution and the profit company will make c) Determine manually the sensitivity range for the profit per tractors. Show your manual calculations d) By inspecting your graph, determine the shadow price for assembly, Explain the rationale to your answer e) Calculate manually the maximum amount a manager should be willing to pay for one additional hour of machine time. Show your calculations f) Determine manually and by inspecting your graph the sensitivity range assembly? Explain rationale your answer