A company that manufactures three products, A, B, and using three machines, M1, M2, and M3, wants to determine the optimal production 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 Crequires M1 and M2. The unit profits on the three products are $7, $8, and $8, respectively. The following linear program is formulated to determine the optimal product mix Maximize St. Z = 7x1 + 8x2 + 3x3 X1 + 2xy + xy S 430 (Machine 1) 3x + 2xy S 460 (Machine 2) X1 + 4x2 $450 (Machine 3) *1, 2, 3 20 where xs, x, and X, are the amounts of products A B, and C and the constraints reflect the available capacities of M1, M2, and Ms. The optimum solution for the problem is as follows: (following figures are hypothetical) optimal solution: X-0, X; -150, X3 - 290 optimal value maximum profit, 2 - 1860 shadow prices 6.0, 7.0, and 0.0 for constraints 1, 2 and 3 respectively reduced costs for X, - 8.0, for x = 0, for x = 0 RANGES ON RIGHT-HAND SIDE (RHS) CONSTRAINTS Row Lower Limit Present Value Upper Limit 230 430 455 2 410 460 860 30 B 400 450 RANGES ON OBJECTIVE FUNCTION COEFFICIENTS Variable Lower Limit Present Value Upper Limit X1 7.0 70 X2 0 8.0 10.0 Xa 3.0 8.0 60 Using the above information answer the following question: Suppose that the capacity of machine 2 can be increased by another 200 minutes at a cost of $250. Is it economical to do so? Select the correct answer. Yanitiniz: An increase in machine 2 capacity will change Z by 7x200 - 1400 dollars. Since the cost of $250 is less than 51400, it is economical to increase machine 2 capacity, An increase in machine 2 capacity will change Z by 2x200 - 400 dollars. Since the cost of $250 is less than $400, it is economical to increase machine 2 capacity An increase in machine 2 capacity will change Z by 0 2000 dollars. Therefore there is no need to change machine 2 capacity An increase in machine 2 capacity will change Z by 150-200 - 30.000 dollars. Since the cost of $250 is less than 524.000, it is economical to increase machine 2 capacity Manitie