How many gallons should goop purchase to maximize profit

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Reference no: EM131876370

Question: Goop Inc needs to order a raw material to make a special polymer. The demand for the polymer is forecasted to be Normally distributed with a mean of 250 gallons and a standard deviation of 125 gallons. Goop sells the polymer for $25 per gallon. Goop's purchases raw material for $10 per gallon and Goop must spend $5 per gallon to dispose off all unused raw material due to government regulations. (One gallon of raw material yields one gallon of polymer.) That is to say, the salvage value is $(-5)/gallon. If demand is more than Goop can make, then Goop sells only what they made and the rest of demand is lost.

1. Suppose Good purchases 150 gallons of raw material. What is the probability that they will run out of raw material?

2. How many gallons should Goop purchase to maximize its expected profit?

3. If Goop purchase the amount of polymer calculated in the previous question. How many sales in gallon will be lost on average?

4. Continued to previous question, what is the expected left over of inventory at the end of the selling season?

5. What is the maximum expected profit?

6. Suppose Goop purchases 300 gallons of raw material. How many gallons of demand on average would remain unfulfilled (expected lost sales)?

7. Suppose Goop purchases 400 gallons of raw material. How many gallon should they expect to disposal? How much money to spend on disposal costs (in dollars) ?

8. Instead of aiming at the maximum profit, suppose Goop wants to ensure that there is a 92% probability that they will be able to satisfy the customer's entire demand. In other words, they set the service level to be 92%. How many gallons of the raw material should they purchase?

9. Continued to previous question, given the 92% service level, what is the expected profit?

Please show all the work for every question and steps in detail.

Reference no: EM131876370

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