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 ​$16 price. The cost of baking a cake is ​$10​, and demand is estimated to be normally​ distributed, with a mean of 30 and a standard deviation of 7.
What is the optimal stocking​ level?

Answer 1

Answer:

optimal stocking level = 30.472

Explanation:

given data

Discount = 50%

Regular price, p = $16

cost of cake, c = $10

Mean = 30

Standard deviation, σ = 7

solution

we get her salvage value that is = 50% of Regular price

salvage value s = 50% of $16

salvage value s =  $8

and

Underage cost will be

Cu = p - c    .......................1

put here value

Cu = $16 - $ 10

Cu = $6

and

Overage cost will be

Co = c - s     ........................2

Co = $10 - $8

Co = $2

so here probability is

P ≤ $\frac{C_{u}}{(C_{u}+C_{o})}$    .....................3

put here value

P ≤ $\frac{6}{(6+2)}$  

P ≤ 0.75

so here Z value for the probability for 0.75 is

Z =  0.6745

and

optimal stocking level will be

optimal stocking level = Mean + ( z × σ )     .....................4

put here value

optimal stocking level = 30 + 0.6745 × 7

optimal stocking level = 30.472