Question

A national pharmacy chain considers selling graduation cards. These cards are typically released in April and need to be sold by the end of June for full value. After June, the remaining cards would be marked down to get sold. For each card, the item cost is $0.89, the regular selling price by the end of June is $3.99, and the marked down price after June is $0.49. The pharmacy's historical demand is normally distributed with a mean of 1.7 million cards and a standard deviation of 0.15 million cards. You would need to show equations, steps, and the final results with units for full credits. Answers are in millions using 5 decimals, e.g. 1.76384 million cards. You should not round up the numbers! For simplicity, all taxes and other costs are not considered. All parts below are based on the optimal order quantity decision in part (a). See Hint below.

(a)[3] To maximize expected profit, how many cards should the pharmacy carry this year?

(b)[2] Sketch the normal demand distribution with details to illustrate the business decision.

(c)[1] What is the expected inventory? (in millions with 5 decimals)

(d)[1] What are the expected sales? (in millions with 5 decimals)

(e)[1] What is the expected profit? (in millions of dollars with 5 decimals) (f)[1] What is the in?stock probability? (5 decimals)

(g)[1] What is the stockout probability? (5 decimals)

Hint: Use the following tables to find the z?value and the corresponding I(z) value.

table 1

?v 0.57571 0.66429 0.75286 0.88571 0.93000

zv = NORM.S.INV(?v) 0.19094 0.42419 0.68351 1.20405 1.47579

table2

zv 0.96324 1.20405 1.38466 1.56527 1.80608

I(zv) 1.05255 1.25969 1.42258 1.59048 1.82013

Answer 1