Answered: Robot Company franchises combination…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Robot Company franchises combination gas and car wash stations throughout the United
States. Robot gives a free car wash for a gasoline fill-up or, for a wash alone, charges
$0.50. Past experience shows that the number of customers that have car washes following
fill-ups is about the same as for a wash alone. The average profit on a gasoline
fill-up is about $0.70, and the cost of the car wash to Robot is $0.10. Robot stays open
14 hours per day.
Robot has three power units and drive assemblies, and a franchisee must select the
unit preferred. Unit I can wash cars at the rate of one every five minutes and is leased
for $12 per day. Unit II, a larger unit, can wash cars at the rate of one every four minutes
but costs $16 per day. Unit III, the largest, costs $22 per day and can wash a car
in three minutes.
The franchisee estimates that customers will not wait in line more than i ve minutes
for a car wash. A longer time will cause Robot to lose the gasoline sales as well as the car
wash sale.
If the estimate of customer arrivals resulting in washes is 10 per hour, which wash unit
should be selected?

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