Question: Problem 2 (75 points) A post office uses 10,000 boxes a year. Carrying costs are 50 cents per box a year, and ordering costs are

Problem 2 (75 points) A post office uses 10,000

Problem 2 (75 points) A post office uses 10,000 boxes a year. Carrying costs are 50 cents per box a year, and ordering costs are $100. The following price schedule applies. Price per Box 1,000 to 3,999 1.20 4,000 to 6,999 1.10 D = 10,000 boxes S = $100 H = $0.50/ box per year a. Determine the optimal order quantity. 2DS H 2(10,000)100 Q = 2,000 boxes TC = H+ S+PD 200 (19000 (2000 (10000 TC 2,000 = 5+ 100 + (1.2 * 10000) = $13,000 2 2000 14000 10000 TO .5+ 100+ (1.1 * 10000) = $12, 250 The best order quantity would be 4,000 boxes because that number allows the lowest price b. The post office opens 250 days per year. Usage appears normally distributed with a standard deviation of 4 boxes per day. Lead time is 4 days. What ROP will provide a lead time service level of 90 percent? (Hint: The average daily usage should be the annual usage divided by the open days per year.)

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