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 $10 price. The cost of baking a cake is $7, and demand is estimated to be normally distributed, with a mean of 25 and a standard deviation of 8. What is the optimal stocking level? Refer to the standard normal table for z-values.

 

The optimal stocking level for the bakery is _______  cakes (round your response to the nearest whole number).

Answer 1

Cost \(c=\$ 7\)

Selling price \(p=\$ 10\)

$$ \begin{aligned} &\text { salvage value } s=\$ 5 \\ &\text { Mean }=25 \end{aligned} $$

Standard deviation \(\sigma=8\)

$$ \begin{aligned} &C_{u}=\text { underage cost }=p-c=\$ 10-\$ 7=\$ 3 \\ &C_{0}=\text { overage cost }=c-s=\$ 7-\$ 5=\$ 2 \\ &P \leq C_{u} /\left(C_{u}+C_{o}\right) \\ &P \leq 3 /(3+2) \\ &=0.6 \end{aligned} $$

By using normsinv() function in excel we to find the correct critical value

The Z value for the probability \(0.6\) is \(0.2533\)

The optimal stocking level is

$$ \begin{aligned} &=\mu+z \sigma \\ &=25+0.2533 * 8=27.02 \end{aligned} $$

The optimal stocking level of bakery is \(27.02\)