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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?

Respuesta :

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

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