A toy store is considering purchasing a popular toy to sell during the holiday season. The toy can be purchased for $2.50 per unit before and up to Christmas. After Christmas, all remaining units can be marked down and sold for $1.00 per unit. The store estimates that the cost of losing goodwill from customers whose demand is not satisfied is $0.35 per customer. The store has three potential sales prices and their associated empirical probability demand distributions as follows:

Sales Price $7.50 - Empirical demand distribution:

Demand: 20, Probability: 0.05

Demand: 24, Probability: 0.10

Demand: 28, Probability: 0.30

Demand: 32, Probability: 0.20

Demand: 36, Probability: 0.25

Demand: 40, Probability: 0.06

Demand: 44, Probability: 0.04

Assuming the store wants to maximize its expected profit, what is the optimal sales price for the toy? --BREAK-- Here is how I attempted to answer this: Evaluate the critical ratio: Cu / (Co + Cu)

1. Cu = Market Price Unit Cost + Unit Goodwill Cost = $7.50 - $2.50 + $0.35 = $5.35
2. Co = Unit Cost Markdown Price = $2.50 - $1.00 = $1.50
3. Cu / (Co + Cu) = $5.35 / ($5.35 + $1.50) = 0.7810219 or 0.78
4. Calculate the cumulative probability:

Demand	f(D)	F(D)
20	0.05	0.05
24	0.10	0.15
28	0.30	0.45
32	0.20	0.65
36	0.25	0.90
40	0.06	0.96
44	0.04	1.00

1. Find where F(D) >= Critical Fractile (0.78)
2. Mean = 20*(0.05)+24*(0.1)+28*(0.3)+32*(0.2)+36*(0.25)+40*(0.06)+44*(0.04) = 31.36
3. F(D) = 0.90, Q=36 Units