Two (2) Questions in this format. Please help in answering both Question 1 and question 2 and completing the tables for both question showing all steps and formula used to find the final answer for each step.

Please show all answers using the 2 decimal places convention (do NOT round an intermediate or final answer to a whole number).

Remember to show all work (including equations used) leading to the final answer.

Question 1 (Empirical Demand Distribution)

The Supermarket Store is about to place an order for Halloween candy. One best-selling brand of candy can be purchased for $ 2.50 per box before and up to Halloween. After Halloween, all the remaining candy can be marked down and sold for $ 1.00 per box. Assume that the loss in goodwill "cost" stemming from customers whose demand is not satisfied is $ 0.35. Three potential sales prices and their associated empirical probability demand distributions are as follows.

Sales Price $ 7.50 - Sales Price $ 8.50 - Sales Price $ 9.50 -

Empirical demand. Empirical demand Empirical demand

distribution. distribution. distribution.

Demand Probability. Demand Probability. Demand Probability

- D -f(D) D - f(D) D - f(D)

20 0.05 20 0.10 20 0.15

24 0.10 24 0.15 24 0.20

28 0.30 28 0.35 28 0.40

32 0.20 32 0.15 32 0.08

36 0.25 36 0.15 36 0.07

40 0.06 40 0.06 40 0.06

44 0.04 44 0.04 44 0.04

You are required to evaluate each sales price by completing the table

Remember to show all work (including equations used) leading to the final answer.

Sales Price. Optimal Stocking Expected Profit. Expected Shortage

Quantity (Q*) in units. E[(Q*)] in $. ES(Q*) in boxes

$ 7.50 ________ _________ ________

$ 8.50 ________ _________ ________

$ 9.50 ________ _________ ________

Question 2 (Normally Distributed Demand)

The Supermarket Store is about to place an order for Halloween candy. One best-selling brand of candy can be purchased at $ 2.50 per box before and up to Halloween. After Halloween, all the remaining candy can be marked down and sold for $ 1.00 per box.

Assume that the loss in goodwill "cost" stemming from customers whose demand is not satisfied is $ 0.35.

The store is considering a price per box (p) of $ 4, $ 5, $ 6, and $ 7. Recognizing that demand is price dependent, through market research the store determines that demand is normally distributed such that if: (a) p=$ 4, mean==50, and standard deviation = =20; (b) p = $ 5, mean==46, and standard deviation = =20; (c) p = $ 6, mean==42, and standard deviation = =20; and (d) p = $ 7, mean==38, and standard deviation = =20.

For each sales price, complete the following table:

Remember to show all work (including equations used) leading to the final answer.

Sales Optimal Stocking Expected Profit Expected Shortage

Price Quantity (Q*) in units. E[(Q*)] in $ ES(Q*) in boxes

$ 4.00 _____________ _____________ ____________

$ 5.00 _____________ _____________ ____________

$ 6.00 _____________ _____________ ____________

$ 7.00 ______________ _____________ ____________