The Outdoor Furniture Corporation manufactures two products, benches and picnic tables, for use in yards and parks. The firm has two main resources: labor and redwood. A linear program has been formulated to solve the problem of how many benches (defined as x₁) and how many picnic tables (defined as x₂) to produce in the next production cycle so as to obtain the largest possible profit. The printout below shows the optimal solution and sensitivity reports for this LP obtained from Excel/Solver.

Use the information from these printouts to answer questions below. Be sure to explain/justify your answers to receive full credit.

a). How many benches and how many picnic tables should be produced to maximize profit? What is the maximum profit? Explain/justify your response. [5 pts]

Note: Consider the changes indicated in parts b, c, and d independently.

b). Suppose that it is possible to increase the amount of labor available by 100 hours. By how much would this increase the total profit? Explain/justify your response. [5 pts]

c). If the profit for a bench increases to $20 per unit, what will the optimal value of x₁ and x₂ be? What will the objective function value be? Explain/justify your response. [5 pts]

d). The production manager has just learned that the supply of redwood is only 3800 feet for the next production cycle, due to some quality problems. What is the effect of this change? What will the new optimal solution and objective function value be? Explain/justify your response.

Microsoft Excel Answer Report Target Cell (Max) Cell Name Original Value Final Value SD$7 Total Profit 0 4250 Adjustable Cells Cell $B$5 $C$5 Name Original Value Final Value 0 125 x2 0 50 Constraints Cell Value Cell SD$10 SD$11 Status Binding Binding Name Formula Slack Labor Used (hours) Redwood Used (feet) 1725 SD$10