Question

Milk is stocked at a grocery store each week. at the end of each week, unsold milk price is reduced by 40% and the store can sell the unsold milk fully at this lower price. if weekly demand for milk is normally distributed with a mean of 200 gallons and standard deviation of 20 gallons, find the price for which a fresh gallon of milk sells. assume that the store has a service level of 95% and purchases milk for $2. 48 per gallon

Answer 1

The selling price that a gallon of milk sells is $5.77 for the given milk store.

What is demand?

The amount of a good that users are willing and competent to acquire at various prices during a certain period of time is known as demand.

Computation of Price:

According to the given information,

Let, the selling price be x.

Salvage Value = 40% of x

$\rm{Salvage Value = 0.40 x$

Cost Price (C.P.) = $2.48

Mean = 200 gallons

Standard Deviation = 20 gallons

Service Level = 95%

Now, find the Cost of underage (Cu):

$C_u = \text{Selling Price - Cost Price}\\\\C_u = x-\ 2.48$

Then, the cost of Overage (Co):

$C_o = \text{Cost Price - Salvage Value}\\\\C_o = \ 2.45 - (0.40 x)$

Now, the service level is:

$\text{Service level} = \dfrac{C_u}{C_u + C_o} \\\\0.95 =\dfrac{x-\ 2.48}{x-\ 2.48 + \ 2.78-0.40x}\\\\x= \ 5.77$

Therefore, the selling price that a gallon of milk sells is $5.77.

To learn more about the selling price, refer to:

brainly.com/question/17960775

#SPJ1