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Unformatted text preview: 1 Assignment 4, STAT220-Winter 2011 Instructor: Kamyar Moshksar Due on March 11th, 2011 Problem 1- A manufacturer of car radios ships them to retailers in cartons of n radios. The profit per radio is is $59.5, less shipping cost of $25 per carton, so the profit is $(59.5 n-25) per carton. To promote sales by assuring high quality, the manufacturer promises to pay the retailer $200 X 2 if X radios in the carton are defective (The retailer is responsible to repair those defective radios.). Suppose radios are produced independently and that %5 of radios are defective. How many radios should be packed per carton to maximize expected net profile per carton? Solution: The expected net profit is E (59 . 5 n- 25- 200 X 2 ) = 59 . 5 n- 25- 200 E ( X 2 ) . We know X ∼ Bi( n,p ) where p = 0 . 05 . So, E ( X 2 ) = V ar ( X ) + ( E ( X )) 2 = np (1- p ) + ( np ) 2 = 0 . 0475 n + 0 . 0025 n 2 . Hence, Expected Net Profit = 50 n- 25- . 5 n 2 ....
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