HELLE AaBbCcDd AaB 3 Heading 1 Heading Heading 6 10 HOTEL TEPAL 11 1230124 15 16 17 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 (5) Sprocket 1 2 2 15 50 Sprocket 2 4 1 20 60 Capacity (hrs/wk) 90 SO 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: XI S 15 Max Sales Sp. 2: X2 520 Machine Time: 2x] + 4x2 5 90 Assembly Time: 2x] S50 Non-negativity: 1 20 + (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 $61. 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. 12 X] SIS Max Sales Sp. 2: X2 S 20 3 s Max Sales Sp.3: Machine Time: 2x] + 482 5 90 Assembly Time: 2x] + X2 550 Non negativity X2 20 Complete the formulation above by filling in the four blanks (b) In December, the problem turns out to be the same as the November problem given in part (a), except that a new packaging process has resulted in an additional requirement that at least 2 sprocket l's must be produced for every sprocket 2 that is produced. Either include below the LP formulation of this new problem, or clearly state how the formulation in part (a) could be changed to deal with the December situation. (2 points) (c) In January, the problem turns out to be the same as the November problem given in part (a), except that the selling price per unit for sprockets 1 and 2 have each decreased by 10%. Either included below the LP formulation of this new problem, or clearly state how the formulation in part(a) could be changed to deal with the January situation. (3 points) (d) In February, the problem turns out to be the same as the November problem given in part (a), except that it is now in February) possible to purchase up to 10 additional hours of machine time at a price of $6 per hour. The $6 per hour cost applies to only the additional 10 hours. Either include below the LP formulation of this new problem, or clearly state how the formulation in part (a) could be changed to deal with the February situation. (6 points) Hint: Add a new decision variable (Y: the number of extra machine hours to produce)