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. 1 2 3 4 5 6 1 15 15 2 4 4 2 P(x) 15 15 15 15 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.) What is the expected profit if four magazines are ordered? (Round your answer to two decimal places.) 24

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.1: Equations
Problem 75E
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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.
1
2
4
5
6
2
1
4
4
2
2
p(x)
15
15
15
15
15
15
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.)
$
What is the expected profit if four magazines are ordered? (Round your answer to two decimal places.)
$
Transcribed Image Text: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. 1 2 4 5 6 2 1 4 4 2 2 p(x) 15 15 15 15 15 15 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.) $ What is the expected profit if four magazines are ordered? (Round your answer to two decimal places.) $
Expert Solution
Step 1

(a) Expected profit if 3 magazine are ordered

     E[X] = i=13 x p(x)

           = 1×215+2×115+3×415

          = 1.0666

 

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