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

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

[tex]\rm{Salvage Value = 0.40 x[/tex]

Cost Price (C.P.) = $2.48

Mean = 200 gallons

Standard Deviation = 20 gallons

Service Level = 95%

Now, find the Cost of underage (Cu):

[tex]C_u = \text{Selling Price - Cost Price}\\\\C_u = x-\$2.48[/tex]

Then, the cost of Overage (Co):

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

Now, the service level is:

[tex]\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[/tex]

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

To learn more about the selling price, refer to:

https://brainly.com/question/17960775

#SPJ1