Question $1$

Problem $727310$:

Do not include anything other than numbers in your responses. For example, do not include comma

or dollar sign in your numbers. As a rule of thumb, keep $2$ decimal places for larger numbers and $3$

decimal places for smaller numbers less than $1.$

A supermarket bakery must decide how many birthday cakes to prepare for the upcoming weekend.

Cakes cost $$40$ each to make, and they sell for $$89$ each. Unsold cakes are sold at $$20$ on Monday,

and typically all the remaining cakes are sold at that price on Monday. Demand is normally distributed

with the mean of $131$ and standard deviation of $26\mathrm{.}2.$ Determine the followings:

Cost of Shortage $($Cs$)$:

Cost of Excess $($Ce$)$:

What is the optimal service level?

What is the corresponding $z$ value?

What is the optimal number of birthday cakes to make for the weekend?A supermarket bakery must decide how many birthday cakes to prepare for the upcoming weekend. Cakes cost $$40$ each to make, and they sell for $$89$ each. Unsold cakes are sold at $$20$ on Monday, and typically all the remaining cakes are sold at that price on Monday. Demand is normally distributed with the mean of $131$ and standard deviation of $26\mathrm{.}2.$ Determine the followings: