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4. Famous Fabricators has the opportunity to supply their customer Service Systems with a key component of the model K47 known as the power core housing. Given the short amount of time available to complete the order, Famous Fabricators only has one opportunity to purchase the raw materials to make the power core housing. The raw materials cost $180 and the profit for selling a power core housing to Service Systems is $260. The exact number of power core housings that Service Systems will purchase is uncertain but follows the distribution given below. Demand Probability 12 14 16 18 0.10 0.18 0.29 0.31 20 0.12 a. Given the information above, how many power core housings do you recommend Famous Fabricators produce if their objective is to maximize their expected profit? Why? b. What is the expected profit for the number of power core housings you chose to produce in part a? c. Suppose you could either reduce the material costs to make a power core housing by $50 or you could increase the profit for each power core housing you sell by $50 which would increase your expected profit more? Or do both options have the same effect on the expected profit? Why?