A manufacturer of industrial sales has production capacity of 1,000 unitsper 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 customershave said that they would be willing to pay $15 per unit if capacity was available onthe last day. About ten days in advance, demand for the high-price segment isnormally distributed with a mean of 250 and a standard deviation of 100. How muchproduction capacity should the manufacturer reserve for the last day? Show theanswer clearly. A manufacturer of industrial sales has production capacity of 1,000 unitsper 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 customershave said that they would be willing to pay $15 per unit if capacity was available onthe last day. About ten days in advance, demand for the high-price segment isnormally distributed with a mean of 250 and a standard deviation of 100. How muchproduction capacity should the manufacturer reserve for the last day? Show theanswer clearly.

Given data is Normal production = 1000 units per day Normal cost = $10×1000=$10000 Spot production = 15000 Spot cost=$15×1000=$15000 Demand = 250 Standard deviation of demand = 100The formula to calculate the probability is given below. p=Spot cost-Normal costSpot production Substituting values p=15000-1000015000p=500015000p=0.33The calculation of production capacity for the last day can be done in excel using the formula shown below. Here 0.33 is the probability, 250 is the mean which is demand, and 100 is the standard deviation. With this formula, the production capacity obtained is 206 units.

Answered: A manufacturer of industrial sales has…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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