QUESTION 3: Linear Programming Formulation (33 points) Acme sells two sprocket assemblies for escalators and elevators. Each type of sprocket must first be machined and then assembled. Unit machining and assembly times, capacity limitations, demand restrictions and revenue-cost data are as follows: Required Hrs/unit Max Unit Machining Assembly Sales Price (S) Sprocket 1 2 2 15 50 Sprocket 2 4 1 20 60 Capacity (hrs/wk) 90 50 Cost $5/hr $4/hr Let xl and x2 represent the number of units of sprockets 1 and 2 to produce, respectively. MAX Z=32x1 + 36x2 Subject to Max Sales Sp. 1: X1 s15 Max Sales Sp. 2: x2 Machine Time: 2x 1 + 4x2 Assembly Time: 2x x2 s 50 Non-negativity: X1, X2 20 s 20 S 90 + (1) Would it be worthwhile to increase the maximum sales level on Sprocket 2 OR to increase the maximum Machine capacity? Justify (2 points) (5) ACME is offered $7 per hour for use of their assembly time by an outside contractor. How much assembly time is it worthwhile to sell? (2 points). (h) If a machine breakdown reduced machining capacity by 20 hours, how would profits be affected? (2 points)