Question

A manufacturer of car radios ships them to retailers in cartons

A manufacturer of car radios ships them to retailers in cartons of n radios. The profit per radio is $59.50, less shipping cost of $25 per carton, so the profit is$(59.5n-25) per carton. To promote sales by assuring high quality, the manufacturer promises to pay the retailer $200X^2 if X radios in the carton are defective. (Theretailer is then responsible for repairing any defective radios.) Suppose radios are produced independently and that 5% of radios are defective. How many radios shouldbe packed per carton to maximize expected net profit per carton?

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