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The demand for a product of Carolina Industries varies greatly from month to month. The probability distribution in the following table, based on the past two years of data, shows the company’s monthly demand. Unit Demand Probability 300 .20 400 .30 500 .35 600 .15 a. If the company bases monthly orders on the expected value of the monthly demand, what should Carolina’s monthly order quantity be for this product? b. Assume that each unit demanded generates $70 in revenue and that each unit ordered costs $50. How much will the company gain or lose in a month if it places an order based on your answer to part (a) and the actual demand for the item is 300 units?

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 5.3, Problem 22E
Textbook Problem
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The demand for a product of Carolina Industries varies greatly from month to month. The probability distribution in the following table, based on the past two years of data, shows the company’s monthly demand.

Unit Demand Probability
300 .20
400 .30
500 .35
600 .15
  1. a. If the company bases monthly orders on the expected value of the monthly demand, what should Carolina’s monthly order quantity be for this product?
  2. b. Assume that each unit demanded generates $70 in revenue and that each unit ordered costs $50. How much will the company gain or lose in a month if it places an order based on your answer to part (a) and the actual demand for the item is 300 units?

a.

To determine

Find Carolina’s monthly order quantity for the product if the company bases monthly orders on the expected value of the monthly demand.

Explanation of Solution

Calculation:

The data represents the probability distributions of company’s monthly demand for the past two years.

The formula for the expected value of a discrete random variable is,

E(x)=μ=xf(x)

b.

To determine

Find the company’s gain or loss in a month if it places an order based on the answer to part (a) and the actual demand for the item is 300 units.

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