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 purchases raw material for $10 per gallon and Goop must spend $5 per gallon to dispose of unused raw material due to government regulations. (One gallon of raw material yields one gallon of polymer.) If demand is more than Goop can make, then Goop sells only what they made, and the rest of demand is lost.

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

2) Suppose Goop purchases 300 gallons of raw material. How many gallons of demand on average would remain unfulfilled?

3) Suppose Goop purchases 400 gallons of raw material. How much should they expect to spend on disposal costs?

4) Suppose Goop wants to ensure that there is a 92% probability that they will be able to satisfy the customer's entire demand. How many gallons of raw material should they purchase?

5) How many gallons should Goop purchase to maximize its expected profit?

Bob's Fly catalog collected forecasts, sales, and demand data for 20 items in one category from its previous catalog. The data is provided below in the table.

For example, their forecast for the first item in the table was 100 units, but it unfortunately only sold 26 units. However, with the last item listed, they sold 341 units but could have sold 569 units if they had ordered enough inventory. For the next catalog, they have an item for which they forecast demand to be 400 units. Suppose they will use that forecast along with the data in the above table to choose a normal distribution to model demand for this product. What mean and standard deviation should they choose?

Demand for Surf World is Poisson with mean 2.5. If they happen to stock 5 copies, what is the expected number of customers who will want to purchase Surf World but will be unable to do so because the bookstore runs out of copies?

Forecast 100 500 150 64 46 210 360 450 190 280 120 70 50 520 230 390 250 170 420 480 340 310 5590 280 Sales Demand 26 26 135 135 51 51 75 75 243 243 329 329 150 150 224 224 104 104 64 46 520 520 240 240 429 433 275 287 187 204 462 517 528 670 374 506 341 569 4803 5393 240 270 162 201 A/F 0.26 0.27 0.34 0.36 0.68 0.73 0.79 0.80 0.87 0.91 0.92 1.00 1.04 1.11 1.15 1.20 1.23 1.40 1.49 1.84 18.38 0.92 0.42 Total Average Standard Deviation 148