Problem 2: Dilbert\'s Department Store is trying to determine how many Hanson T-

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Problem 2: Dilbert's Department Store is trying to determine how many Hanson T-shirts to order. Currenty, the shirts are sold for $19. But, if there are any remaining (unsold) shirts, Dilbert's will later offer progressively higher price discounts-starting with a discount of 10%, then a 20% discount, 40% discount, 50% discount, and finally a 60% discount. Any leftover shirts after the 60% discount price will be donated. Dilbert's believes that demand at the full price of $19 is Normally distributed. It has gathered historical denand data over the past 36 months (see Spreadsheet·Dilbert, data ) Demnand at various discounts depends on the actual demand at full price; Dilbert's assumes that demand at each discount level is a fixed multiple of the actual full price demand. These multiples are shown in the following table Discount Multiple 10% 20% 0.4 0.7 1.1 50% 60% 50 For example, suppose the actual full price demand turns out to be 2,000 T-shirts and this demand is less than Dilbert's stocking quantity when Dilberts, discounts the price by 10%, it will realize an additional demand of 2,000*0.4-800 T-shirts. If it has any left-over T-shirts after selling at its 10% price discount it will increase the discount to 20%, and realize an additional demand of 2,000-0.7-1,400 T-shirts, and The T-shirt manufacturer offers an all-units quantity discount on T-shirts purchased. Dilbert's unit cost of purchasing T-shirts depends on the number of T-shirts purchased as shown in the table below Unit $15.00 1500 514.25 $13.54 4

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