A creamery shop sells its special ice cream for $4.50 a quart. It costs them $3.00 a quart to make it. The daily demand for this flavor is normally distributed with a mean of 35 quarts and a standard deviation of 4 quarts. Unsold ice cream is sold each day to a local restaurant at $1.50 per quart. What is the service level and corresponding optimal stocking level?

Answer and Explanation:

The computation of the service level and the corresponding optimal stocking level is shown below:

Given that

Selling price = SP = $4.50

Cost price = CP  = $3.00

So,

Salvage value =  V  = $1.50

Average daily demand (d) = 35 quarts

The  standard deviation of daily demand  = 4 quarts

based on the above information

Overage cost = (Co) is

= CP - V

= $3.00 - $1.50

= $1.50

Now

Underage cost= (Cu)

= SP - CP

= $4.50 - $3.00

= $1.50

So,  

Service level is

= Cu ÷ (Co + Cu)

= 1.50 ÷ (1.50 + 1.50)

= 1.50 ÷ 3.00

= 0.50

= 50%

Now

At 50 % service level, the value of Z is 0

So,

Optimal stocking level is

= d + Z × standard deviation

= 35 + (0  × 4)

= 35 + 0  

= 35 quarts

if you use only 25 for your entertainment and only 200 for the groceries that you really need and take out the 50 per month for the computer then that should be enough