Solution Question 7.20

Solution Question 7.20 - Note that, X 1 and X 2 are random...

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EMGT 269 – Elements of Problem Solving and Decision Making Solution by Instructor: Dr. J. Rene van Dorp SOLUTION QUESTION 7.20: A company owns two different computers, which are in separate buildings and operated entirely separately. Based on past history, Computer 1 is expected to breakdown 5.0 times a year , with a variance of 6 , and costing $200 per breakdown . Computer 2 is expected to breakdown 3.6 times per year , with a variance of 7 , and costing $165 per breakdown . What is the company’s expected cost for computer breakdowns and the variance of the breakdown cost? What assumption must you make to find the variance? Is this a reasonable assumption?
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EMGT 269 – Elements of Problem Solving and Decision Making Solution by Instructor: Dr. J. Rene van Dorp SOLUTION: Definitions: X 1 = Annual Number of Breakdowns of Computer 1 c 1 = Cost per Breakdown of Computer 1 ($200) X 2 = Annual Number of Breakdowns of Computer 2 c 2 = Cost per Breakdown of Computer 2 ($165) TC = Annual Total Cost of Computer Breakdowns
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Unformatted text preview: Note that, X 1 and X 2 are random variables (i.e. their values are uncertain) and c 1 and c 2 are constant values. From the text, we conclude: TC = c 1 X 1 + c 2 X 2 (A LINEAR RELATIONSHIP!) Conclusion: TC is a random variable (its value is uncertain). EMGT 269 Elements of Problem Solving and Decision Making Solution by Instructor: Dr. J. Rene van Dorp A. Because of the Linear Relationship we have: E[TC] = E[c 1 X 1 + c 2 X 2 ] = c 1 E[X 1 ]+ c 2 E[X 2 ] From the text we have: c 1 = $200, c 2 = 165, E[X 1 ] = 5 and E[X 2 ] = 3.6. Hence: E[TC] = $200 x 5 + $165 x 3.6 = $ 1594 B. With an assumption of independence between X 1 and X 2 are we have: Var[TC] = Var[c 1 X 1 + c 2 X 2 ] = (c 1 ) 2 Var[X 1 ]+ (c 2 ) 2 Var[X 2 ] From the text we have: c 1 = $200, c 2 = 165, Var[X 1 ] = 6 and E[X 2 ] = 7. Hence: Var[TC] = ($200) 2 x 6 + (165) 2 x 7 = ($) 2 430575 Standard Deviation TC: 430575 = $656.18 IS THIS ASSUMPTION OF INDEPENDENCE REASONABLE?...
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Solution Question 7.20 - Note that, X 1 and X 2 are random...

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