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2. A company that manufactures three products, A, B, and C, using three machines, M1, M2 and M3, wants to determine the optimal schedule that maximizes the total profit. Product A has to be processed by machines M1, M2, and M3, product B requires M1 and M3, while product C requires M1 and M2. The unit profits in the three products are $8, $4, and $10, respectively. The following linear program is formulated to determine the optimal product mix: Max Z= 4A + 2B + 5C Subject to: 2A + 4B + 2C 5 870 (Machine 1) 6A + 4C S 920 (Machine 1) 2A + 8B 5 900 (Machine 1) Optimal solution: A=0, B=100, C-230 Optimal. Value: Z= 2700 Dual values: Y1 = 1, Y2= 2, Y3=0 Ranges on objective Function Coefficients Variable Lower Present Value Upper Limit Limit A 8 14 B 0 4.0 20.0 6.0 10.0 Restriction Ranges RHS Constant Lower Present Limit Value 860 860 820 920 800 900 Upper Limit 910 1720 1 2 3 a) Because of an increase in the cost of raw material used for product C, its unit profit drops to $8. Determine the new optimal solution and the maximum profit. b) Suppose it is possible to increase the capacity of one of the machines. Which one would you recommend for expansion and why? c) Due to an improvement in product design, the unit profit on product A can be increased to $12. Is it worthwhile producing product A now? Explain d) Suppose the capacity of machine 2 can be increased by another 200 minutes at a cost of $250. Is it economical to do so? Explain e) A new product will be manufactured with the following requirements: 4 hours on machine one, 6 hours on machine three and income of $7.00. Would be worthy to produce the new product? Why? Instructions 1. Procedure (15 points, 3 points each) 2. Results (5 points, 1 point each)