Letting t=number of 20,000 railroad tank cars in the​ fleet, 2t−4 5,000​-gallon railroad tank​ cars, and −3t+27 10,000 gallon railroad tank cars will be in the fleet for a certain range of t. The cost of leasing a 5,000​-gallon tank car is ​$550 per​month, a 10,000​-gallon tank car is ​$650 per​ month, and a 20,000​-gallon tank car is ​$1250

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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A chemical manufacturer wants to lease a fleet of
23
railroad tank cars with a combined carrying capacity of
250,000
gallons. Tank cars with three different carrying capacities are​ available:
5,000
​gallons,
10,000
​gallons, and
20,000
gallons. Letting
t=number
of
20,000
railroad tank cars in the​ fleet,
2t−4
5,000​-gallon
railroad tank​ cars, and
−3t+27
10,000
gallon railroad tank cars will be in the fleet for a certain range of t. The cost of leasing
a
5,000​-gallon
tank car is
​$550
per​month,
a
10,000​-gallon
tank car is
​$650
per​ month, and a
20,000​-gallon
tank car is
​$1250
per month. Which of the solutions to the number of each type of tank car in the fleet would minimize the monthly leasing​ cost?
 
5,000​-gallon
tank​ cars,
 
10,000​-gallon
tank​ cars, and
 
20,000​-gallon
tank cars.
​(Simplify your answers. Type whole​ numbers.)
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