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

optimal stocking level = 30.472

Step-by-step 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 ≤
`(C_(u))/((C_(u)+C_(o)))` .....................3

put here value

P ≤
`(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