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(4.) Suppose you are running a manufacturing plant building computer chips for smart phones. You supply K chips per day to your customer. The manufacturing process is not perfect, however, and with probability p each chip produced is faulty (the state of all chips are mutually independent). Unfortunately it is not known whether a chip is faulty until the customer assembles it into a phone. As a result, you must reimburse the customer Sr for each faulty chip. Suppose that a single days run of manufacturing costs you Sm (a) The number of faulty chips produced each day is a random variable, F. What is its distribution? (b) Use your answer to part (a) to compute your expected daily costs. (c) Suppose that if you spend more in manufacturing costs m, you can reduce the probability p that any given chip is faulty. Specifically, suppose that p -e-am where a 〉 0·What is the value of m that minimizes your expected daily cost? (Justify your answer) (d) What is the probability of a faulty chip, and the expected daily cost you incur from faulty chips, if you employ the optimal value of m from part (c)?

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