A chemical manufacturer wants to lease a fleet of 26 railroad tank cars with a combined carrying capacity of 504,000 gallons. Tank cars with three different carrying capacities are available: 9,000 gallons, 18,000 gallons, and 36,000 gallons. Letting t=number of 36,000 railroad tank cars in the fleet, 2t−4 9,000-gallon railroad tank cars, and −3t+30 18,000 gallon railroad tank cars will be in the fleet for a certain range of t. The cost of leasing a 9,000-gallon tank car is $550 permonth, an 18,000-gallon tank car is $750 per month, and a 36,000-gallon tank car is $950 per month. Which of the solutions to the number of each type of tank car in the fleet would minimize the monthly leasing cost? 9,000-gallon tank cars, 18,000-gallon tank cars, and 36,000-gallon tank cars. (Simplify your answers. Type whole numbers.)
A chemical manufacturer wants to lease a fleet of 26 railroad tank cars with a combined carrying capacity of 504,000 gallons. Tank cars with three different carrying capacities are available: 9,000 gallons, 18,000 gallons, and 36,000 gallons. Letting t=number of 36,000 railroad tank cars in the fleet, 2t−4 9,000-gallon railroad tank cars, and −3t+30 18,000 gallon railroad tank cars will be in the fleet for a certain range of t. The cost of leasing a 9,000-gallon tank car is $550 permonth, an 18,000-gallon tank car is $750 per month, and a 36,000-gallon tank car is $950 per month. Which of the solutions to the number of each type of tank car in the fleet would minimize the monthly leasing cost? 9,000-gallon tank cars, 18,000-gallon tank cars, and 36,000-gallon tank cars. (Simplify your answers. Type whole numbers.)
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
A chemical manufacturer wants to lease a fleet of
26
railroad tank cars with a combined carrying capacity of
504,000
gallons. Tank cars with three different carrying capacities are available:
9,000
gallons,
18,000
gallons, and
36,000
gallons. Letting
t=number
of
36,000
railroad tank cars in the fleet,
2t−4
9,000-gallon
railroad tank cars, and
−3t+30
18,000
gallon railroad tank cars will be in the fleet for a certain range of t. The cost of leasing
a
9,000-gallon
tank car is
$550
permonth,
an
18,000-gallon
tank car is
$750
per month, and a
36,000-gallon
tank car is
$950
per month. Which of the solutions to the number of each type of tank car in the fleet would minimize the monthly leasing cost?9,000-gallon
tank cars,
18,000-gallon
tank cars, and
36,000-gallon
tank cars.(Simplify your answers. Type whole numbers.)
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