A manufacturer of industrial sales has production capacity of 1,000 units per day. Currently, the firm sells production capacity for $10 per unit. At this price, all production capacity gets booked about one week in advance. A group of customers have said that they would be willing to pay $15 per unit if capacity was available on the last day. About ten days in advance, demand for the high-price segment is normally distributed with a mean of 250 and a standard deviation of 100. How much production capacity should the manufacturer reserve for the last day? Show the answer clearly.

A manufacturer of industrial sales has production capacity of 1,000 units per day. Currently, the firm sells production capacity for $10 per unit. At this price, all production capacity gets booked about one week in advance. A group of customers have said that they would be willing to pay $15 per unit if capacity was available on the last day. About ten days in advance, demand for the high-price segment is normally distributed with a mean of 250 and a standard deviation of 100. How much production capacity should the manufacturer reserve for the last day? Show the answer clearly.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter10: Introduction To Simulation Modeling

Section10.5: Introduction To @risk

Problem 20P: Use @RISK to analyze the sweatshirt situation in Problem 14 of the previous section. Do this for the...

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In Problem 12 of the previous section, suppose that the demand for cars is normally distributed with mean 100 and standard deviation 15. Use @RISK to determine the best order quantityin this case, the one with the largest mean profit. Using the statistics and/or graphs from @RISK, discuss whether this order quantity would be considered best by the car dealer. (The point is that a decision maker can use more than just mean profit in making a decision.)
Use @RISK to analyze the sweatshirt situation in Problem 14 of the previous section. Do this for the discrete distributions given in the problem. Then do it for normal distributions. For the normal case, assume that the regular demand is normally distributed with mean 9800 and standard deviation 1300 and that the demand at the reduced price is normally distributed with mean 3800 and standard deviation 1400.
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A grocer purchases plums for $2.95 per pound and sells them for $4.62 per pound. At the end of the sales cycle, leftover plums are sold for a closeout price of $1.76 per pound. The grocer purchases 10,380 pounds of plums. Expected demand is normally distributed with a mean of 8,304 pounds and a standard deviation of 1,038. What is the grocer's expected profit?
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Suppose that the manager of a construction supply house determined from historical recordsthat demand for sand during lead time averages 50 tons. In addition, suppose the managerdetermined that demand during lead time could be described by a normal distribution thathas a mean of 50 tons and a standard deviation of 5 tons. Answer these questions, assumingthat the manager is willing to accept a stockout risk of no more than 3 percent:a. What value of z is appropriate?
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