A small furniture manufacturer produces four products. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. The assembly time, finishing time, and the inspection time for each unit of each product are provided in the table below. The unit cost, selling price, and the minimum demand for each product are also provided.

Hours required to produce one unit Product 1 Product 2 Product 3 Product 4 Available hours Assembly time 3 2 2.5 3 1100 Finishing time 2.5 1 1.5 2 850 Inspection time 1.5 0.5 0.5 1 390 Cost per unit $75 $65 $55 $45 Selling Price per unit $265 $245 $250 $232 The minimum demand (units) 30 60 50 80 To keep a balance, the number of product 4 units produced should be at least twice the number of product 1 units. Also, the number of product 4 units at most twice the number of product 3 units. a) Formulate a linear programming model for this problem. Clearly define the variables, objective function, and constraints. b) Solve the problem using Excel or Excel QM and answer the following i) What is the optimal solution to this LP problem?

ii) Would the optimal solution change if the Selling price of product 2 decreases by $ 20 and all other products are unchanged? Explain