9- Demand for It-is-Hot-Outside fresh ice-cream is (continuous) uniform between 55 and 255 lbs. Profit on each pound of ice-cream is $16. This ice-cream is made in one batch at the begging of the day and any left-over ice cream at the end of the day will be discarded. It costs about $9 to prepare a pound of ice-cream. How much ice-cream (in lbs) should be prepared at the beginning of the day in order to maximize the profit

The quantity of  ice-cream (in lbs) that should be prepared at the beginning of the day in order to maximize the profit is 183 ice cream.

First step is to calculate the service level using this formula

Service level = Cs/(Cs+Ce)

Where:

Cost of shortage (Cs) = $16

Cost of excess (Ce) = $9

Let plug in the formula

Service level= 16/(16+9)

Service level= 16/25

Service level= 0.64

Second step is to calculate the optimal quantity using this formula

Optimal quantity=Lower limit + Service level × (Upper limit - Lower limit)

Where:

Lower limit = 55

Upper limit = 255

Service level= 0.64

Let plug in the formula

Optimal quantity= 55 + 0.64 × (255-55)

Optimal quantity= 55 + (0.64 × 200)

Optimal quantity= 55 + 128

Optimal quantity= 183

Inconclusion the quantity of  ice-cream (in lbs) that should be prepared at the beginning of the day in order to maximize the profit is 183 ice cream.

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183

Explanation:

Based on the information given in the question,

Cost of excess (Ce) = 9$

Cost of shortage (Cs) = 16$

Service level = Cs/(Cs+Ce)

= 16/(16+9)

= 16/25

= 0.64

Lower limit = 55

Upper limit = 255

We then calculate the optimal quantity which will be:

= Lower limit + Service level × (Upper limit - Lower limiit)

= 55 + 0.64 × (255-55)

= 55 + (0.64 × 200)

= 55 + 128

= 183

Therefore, to maximize profit, 183 ice cream should be prepared.

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