The village board of Park City, Utah, arranges for the clearing of all snow in city streets. Weekly snowfall during the winter is normally distributed with a mean of 10 inches and a standard deviation of 4 inches. The board is considering a long term contract with a snow removal company. The long- term contract costs $1000 per truck per week. Thus, if the board signs a long-term contract for 12 inches, they pay $12,000 per week whether the trucks are used or not. Each truck is capable of clearing 1 inch of snow per week. If snowfall in a week exceeds the quantity that can be handled by the trucks included in the long term lease, the board must make emergency arrangements at a cost of $2,500 for each additional truck brought in. For how many trucks should the board sign a long term contract?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter9: Decision Making Under Uncertainty
Section: Chapter Questions
Problem 30P
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The village board of Park City, Utah, arranges for the clearing of all snow in
city streets. Weekly snowfall during the winter is normally distributed with
a mean of 10 inches and a standard deviation of 4 inches. The board is
considering a long term contract with a snow removal company. The long-
term contract costs $1000 per truck per week. Thus, if the board signs a
long-term contract for 12 inches, they pay $12,000 per week whether the
trucks are used or not. Each truck is capable of clearing 1 inch of snow per
week. If snowfall in a week exceeds the quantity that can be handled by
the trucks included in the long term lease, the board must make
emergency arrangements at a cost of $2,500 for each additional truck
brought in.
For how many trucks should the board sign a long term contract?
Transcribed Image Text:The village board of Park City, Utah, arranges for the clearing of all snow in city streets. Weekly snowfall during the winter is normally distributed with a mean of 10 inches and a standard deviation of 4 inches. The board is considering a long term contract with a snow removal company. The long- term contract costs $1000 per truck per week. Thus, if the board signs a long-term contract for 12 inches, they pay $12,000 per week whether the trucks are used or not. Each truck is capable of clearing 1 inch of snow per week. If snowfall in a week exceeds the quantity that can be handled by the trucks included in the long term lease, the board must make emergency arrangements at a cost of $2,500 for each additional truck brought in. For how many trucks should the board sign a long term contract?
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