7. (a) (10 Points) The McCormick Hardware Store places one order for riding lawn mowers each February. The lawn mowers being purchased this year cost $300 and sell for $425. In the past, McCormick has always been able to sell all its surplus mowers during the September "endofsummer\" sale. The sales price for any surplus mowers this year is 5250. If the following probability distribution for demand is assumed, how many mowers should be ordered? Probabilit (bl (10 points) What is McCormick's expected profit if they order 4 mowers? (c) (10 Points) How many gallons should Goop purchase to maximize its expected profit? Note: Round your answer to the nearest integer. 4. (10 Points) A newsvendor orders the quantity that maximizes expected profit for two products, X and Y. The critical ratio for both products is 0.8. The demand forecast for both products is 9,000 units and both are normally distributed. Product X has more uncertain demand in the sense that it has the larger standard deviation. Of which of the two products does the newsvendor order more? Product X because it has less certain demand. Product Y because it has more certain demand. The order quantities are the same because they have the same critical ratio. 0 o o o More information is needed to determine which has the higher order quantity. 5. (10 Points) Product X has a higher standard deviation of demand, and therefore its optimal order quantity is greater given the same mean and critical ratio.(10 Points) Suppose the newsvendor model describes a firm's operations decision. Is it possible to have positive stockout probability and positive expected leftover inventory? Choose the best answer. 0 No. If there is leftover inventory. then a stockout doesn't occur. 0 No. lfthe stockout probability is positive, then expected inventory must be negative. 0 No. Actual demand can differ from sales. 0 Yes. A firm does not stock out and have leftover inventory at the same time, but the stockout probability can be positive even though there is positive expected leftover inventory. 0 Yes, as long as the underage cost is greater than the overage cost. 6. (10 Points) A company uses the newsvendor model to manage its inventories and faces normally distributed demand. The company decides to order a quantity that exactly equals the mean of its demand forecast. Which of the following is true regarding this company's performance measures? There is a 0.50 probability that there is enough inventory to serve all demand. Expected inventory equals 50 percent of the mean of the demand forecast. The stockout probability is 0.25. o o o 0 Expected inventory is 0. CM 235 - HW 8 - FALL 2022 1. (10 Points} A convenience store purchases magazines for $1.25 and sells them for $5. At the end of the month, each unsold magazine can be returned to the publisher for a $0.50 refund. What is the overage cost for a magazine? Note: Round your answer to 2 decimal places. 2. (10 Points) A store owner has determined that the overage cost for a product is $70 and the underage cost is $65. What is the store owner's critical ratio? Note: Round your answer to 3 decimal places. 3. 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 of all unused raw material due to government regulations. If demand is more than Goop can make, then Goop sells only what they made and the rest of demand is lost. (a) (10 Points) Suppose Goop purchases 150 gallons of raw material. What is the probability that they will run out of raw material? Note: Use Table 13.4 from Chapter 13 of the textbook and round your answer to 2 decimal places. (b) (10 Points) Suppose Goop wants to ensure that there is a 92% probability that they will be able to satisfy the customer's entire demand. can: How many gallons of the raw material should they purchase? Note: Use Table 13.4 from Chapter 13 of the textbook and round your answer to the Q: ______ nearest integer