Question

Henrique​ Correa's bakery prepares all its cakes between 4 A.M.and 6 A.M.so they will be fresh when customers arrive.​ Day-old cakes are virtually always​ sold, but at a​ 50% discount off the regular ​$8 price. The cost of baking a cake is ​$5​, and demand is estimated to be normally​ distributed, with a mean of 20 and a standard deviation of 7. What is the optimal stocking​ level?

Answer 1

Answer:

24.7215

Explanation:

Given;

Discount = 50%

Regular price, p = $8

cost of cake, c = $5

salvage value, s = 50% of $8 = $4

Mean = 20

Standard deviation, σ = 7

Now,

Underage cost, Cu = p - c

= $8 - $5

= $3

Overage cost, Co = c - s

= $5 - $4

= $1

P ≤ $\frac{C_{u}}{(C_{u}+C_{o})}$

P ≤  $\frac{3}{(3+1)}$

P ≤ 0.75

The Z value for the probability 0.75 is 0.6745

The optimal stocking level = Mean + ( z × σ )

= 20 + 0.6745 × 7

= 24.7215