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A small market orders copies of a certain magazine for its magazine rack each week. Let X= demand for the magazine, with the following pmf. 3 X P(x) 1 1 16 2 2 16 ✓ 4 16 4 4 16 5 6 3 2 16 16 Suppose the store owner actually pays $2.00 for each copy of the magazine and the price to customers is $4.00. If magazines left at the end of the week have no salvage value, is it better to order three or four copies of the magazine? [Hint: For both three and four copies ordered, express net revenue as a function of demand X, and then compute the expected revenue.] What is the expected profit if three magazines are ordered? (Round your answer to two decimal places.) $ x What is the expected profit if four magazines are ordered? (Round your answer to two decimal places.) $ X How many magazines should the store owner order? 3 magazines O 4 magazines

A small market orders copies of a certain magazine for its magazine rack each week. Let X= demand for the magazine, with the following pmf. 3 X P(x) 1 1 16 2 2 16 ✓ 4 16 4 4 16 5 6 3 2 16 16 Suppose the store owner actually pays $2.00 for each copy of the magazine and the price to customers is $4.00. If magazines left at the end of the week have no salvage value, is it better to order three or four copies of the magazine? [Hint: For both three and four copies ordered, express net revenue as a function of demand X, and then compute the expected revenue.] What is the expected profit if three magazines are ordered? (Round your answer to two decimal places.) $ x What is the expected profit if four magazines are ordered? (Round your answer to two decimal places.) $ X How many magazines should the store owner order? 3 magazines O 4 magazines

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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### Magazine Ordering and Profit Analysis A small market orders copies of a certain magazine for its magazine rack each week. Let \( X \) represent the demand for the magazine, which follows the probability mass function (pmf) outlined below: | \( x \) | 1 | 2 | 3 | 4 | 5 | 6 | |-------------|----|----|----|----|----|----| | \( p(x) \) | 1 | 2 | 4 | 4 | 3 | 2 | | | 16 | 16 | 16 | 16 | 16 | 16 | Suppose the store owner actually pays $2.00 for each copy of the magazine and sells it to customers for $4.00. If magazines left at the end of the week have no salvage value, we need to determine whether it is better to order three or four copies. To answer this, let's calculate the expected profit for ordering three copies and four copies. ### Expected Profit Calculation 1. **For 3 Magazines Ordered:** - Probability of selling 1 magazine: \( \frac{1}{16} \) - Probability of selling 2 magazines: \( \frac{2}{16} \) - Probability of selling 3 magazines: \( \frac{4}{16} \) - Profit = Revenue - Cost \( \text{Revenue: } 3 \text{ (sold)} \times 4 \text{ (price)} = 12 \text{, Cost: } 3 \times 2 = 6 \) Profit = \( 12 - 6 = 6 \) \( E(Profit) = \sum_x p(x) \times (\text{Profit for selling x magazines}) \) \( E(Profit) = \frac{1}{16}(2 - 6) + \frac{2}{16}(4 - 6) + \frac{4}{16}(6 - 6) = \frac{1}{16}(6) + \frac{2}{16}(8) + \frac{4}{16}(12 - 4) + \frac{4}{16}(-2) \) \( E(Profit) = (0.125) + (0.25
Transcribed Image Text:### Magazine Ordering and Profit Analysis A small market orders copies of a certain magazine for its magazine rack each week. Let \( X \) represent the demand for the magazine, which follows the probability mass function (pmf) outlined below: | \( x \) | 1 | 2 | 3 | 4 | 5 | 6 | |-------------|----|----|----|----|----|----| | \( p(x) \) | 1 | 2 | 4 | 4 | 3 | 2 | | | 16 | 16 | 16 | 16 | 16 | 16 | Suppose the store owner actually pays $2.00 for each copy of the magazine and sells it to customers for $4.00. If magazines left at the end of the week have no salvage value, we need to determine whether it is better to order three or four copies. To answer this, let's calculate the expected profit for ordering three copies and four copies. ### Expected Profit Calculation 1. **For 3 Magazines Ordered:** - Probability of selling 1 magazine: \( \frac{1}{16} \) - Probability of selling 2 magazines: \( \frac{2}{16} \) - Probability of selling 3 magazines: \( \frac{4}{16} \) - Profit = Revenue - Cost \( \text{Revenue: } 3 \text{ (sold)} \times 4 \text{ (price)} = 12 \text{, Cost: } 3 \times 2 = 6 \) Profit = \( 12 - 6 = 6 \) \( E(Profit) = \sum_x p(x) \times (\text{Profit for selling x magazines}) \) \( E(Profit) = \frac{1}{16}(2 - 6) + \frac{2}{16}(4 - 6) + \frac{4}{16}(6 - 6) = \frac{1}{16}(6) + \frac{2}{16}(8) + \frac{4}{16}(12 - 4) + \frac{4}{16}(-2) \) \( E(Profit) = (0.125) + (0.25
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