Henrique Correa\'s bakery prepares all its cakes between 4a 6am so they will be

Question

Henrique Correa's bakery prepares all its cakes between 4a 6am so they will be fresh when customers arrive. 50% discount off the regular price of $10. The cost of baking a cake is $6. At the end of the day, leftover cakes are always sold, but at a 1. Suppose demand is estimated to be uniformly distributed between 20 30 cakes. How many cakes should the company bake each morning? 2. Suppose demand is estimated to be the following. How many cakes should the company bake each morning? What is Henrique's expected daily profit Demand Probability 15 10 20 15 30 40 35 30 45 05

Explanation / Answer

Cost per unit = $6
Selling Price = $10
Salvage Value = $10 x 50% = $5

Cu = Cost of underage (loss by keeping one unit less than the demand) = Selling Price - Cost = $10 - $6 = $4
Co = Cost of overage (loss by keeping one unit more than demand) = Cost - Salvage value = $6 - $5 = $1

Critical Ratio = Cu / (Co+Cu) = 4 / (4+1) = 0.80

(1)

Demand ~ Uniform(20, 30)

Optimal baking quantity = 20 + Critical Ratio x (30 - 20) = 20 + 0.80 x 10 = 28

(2)

The critical ratio is covered by cumulativve probability 0.95 at Demand=35. So, the optimal baking quantity should be 35.

* 15 x 4 - 20 x 1 = 40
** 20 x 4 - 15 x 1 = 65
*** 30 x 4 - 5 x 1 = 115
**** 35 x 4 = 140
***** 40 x 0.1 + 65 x 0.15 + 115 x 0.40 + 140 x 0.30 + 140 x 0.05 = 108.75

Demand 15 20 30 35 45 Probability 0.10 0.15 0.40 0.30 0.05 Cumulative Probability 0.10 0.25 0.65 0.95 1.00

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