PEC is a manufacturer of party hats and costumes. 80% of its yearly sales occur over a 6-week period. One of its popular products is the Elvis wig. The wig is produced in China so PEC must make a single order well in advance of the upcoming season. Ryan the owner of PEC expects demand to be 25,000 Elvis wigs and this expectation is unbiased. Assume demand is normally distributed with a standard deviation of 6000 wigs. PEC sells the Elvis wig for $25/unit and its unit production cost is $6. Assume leftover inventory is liquidated for $2.5/unit
a. Suppose PEC orders 40,000 wigs. What is the probability of a stock out (That the elvis wig demand will be more than 40,000 wigs)? What is the chance that PEC will have to liquidate 10,000 or more wigs with a discounter?
b. How many Elvis wigs should PEC order from its chinese manufacturer to minimize expected total overage and shortage costs?
c. For your chosen order quantity in b, will the expected (average) sales of Elvis wigs be smaller than, bigger than, or equal to 25,000? Explain.
d. Suppose you pick an order quantity Q > 25,000 for your order quantity, you are told that the expected number of shortages (expected lost sales) over the season will be positive and equal to 490 wigs. How many wigs do you expect to tsell in the selling season? How many wigs do you expect to have leftover at the end of the season?