2 4 1 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 ($) Sprocket 1 2 15 SO Sprocket 2 20 60 Capacity (hrs/wk) 90 50 Cost $5/ht $ 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: X SIS Max Sales Sp. 2: 5 20 Machine Time: 2x1 + 4x2 S 90 Assembly Time: X2 S 50 Non-negativity: 20 X2 2x1 + X1 (a) In November, Acme introduces a third type of sprocket (Sprocket 3). To produce one sprocket 3 requires 3 hours of machining and three hours of assembly. The maximum sales of sprocket 3 is 10 units. The selling price of a sprocket 3 is 561. The above formulation can be modified to take account of the new product. The new formulation is: Let x1, x2 and x3 represent the number of units of sprockets 1, 2 and 3 to produce, respectively. MAX Z = 32X1 + 36x2 Subject to Max Sales Sp. 1: