Betty Cooker runs a bakery in San Francisco that specializes in her famous Black

Question

Betty Cooker runs a bakery in San Francisco that specializes in her famous Black Forest cakes. These cakes come with four kinds of frostings—Vanilla, Chocolate, Raspberry and Devilicious. She estimates that the daily demand for each type of cake is independent, and is Normally distributed with mean 50 and standard deviation 20. Each customer wants to buy exactly one cake. Customers who favor a particular type of frosting will not buy any other if their preferred frosting is out of stock. Every day in the morning, Betty Cooker and her team of bakers prepare a fresh batch of the cakes for sale that day. Her costs to bake and top each cake are $5. Each cake sells for $15. Betty’s Bakery prides itself on its fresh assortment, so cakes not sold by the end of that day are given away to a soup kitchen for the homeless.

Suppose Betty wants to bake enough cakes so that she can be 97.5% sure that she can satisfy the demand for all of her customers. How many cakes with Devilicious frosting should she prepare daily in the morning?

A. 109.2 B. 99.2 C. 79.2 D. 89.2

How many should she bake if she wants to maximize expected profit?

A. 49 B. 39 C. 59 D. 69

What are her expected profits for the order quantity that maximizes expected profit (the quantity you just calculated)?

A. 390.95 B. 490.95 C. 290.95 D. 190.95

Explanation / Answer

Stock-In Probability = 97.5

Z Value at 97.5 = 1.96

Mean = 50

Std Dev = 20

A) Number of Cakes she should prepare = Mean + Z*Std Dev = 50+ 1.96*20 = 89.2 (Option D)

Underage Cost = Selling Price - Cost Price = 15-5 = 10

Overage Cost = Cost Price - Salvage Price = 5-0 = 5

Critical Ratio = Underage Cost/(Underage Cost+Overage Cost) = 10/(10+5) = 0.6667

Z value at 0.6667 = 0.43

B) Quantity for Maximum Profit = Mean + Z*Std Dev = 50 + 0.43*20 = 58.6 ~ 59 (Option C)

Loss Function value at Z = 0.43 is 0.2203

Expected Loss Sales = Std Dev*Loss Function Value = 20*0.2203 = 4.406

Expected Sales = Expected Demand-Expected Loss Sale = 50-4.4 = 45.6

Expected Left over Inventory = 58.6-45.6 = 13

C) Expected Profit = (Underage Cost*Expected Sales) + Overage Cost*Expected Left over Inventory = 10*45.6-5*13 = 391 or 390.95 (Option A)

Please Like & Provide your reviews in comments. :-)

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.