A chemical manufacturer wants to lease a fleet of 25 railroad tank cars with a combined carrying capacity of 260,000 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 -2 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 $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? 5,000-gallon tank cars, 10,000-gallon tank cars, and 20,000-gallon tank cars. (Simplify your answers. Type whole numbers.)

A chemical manufacturer wants to lease a fleet of 25 railroad tank cars with a combined carrying capacity of 260,000 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 -2 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 $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? 5,000-gallon tank cars, 10,000-gallon tank cars, and 20,000-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 25 railroad tank cars with a combined carrying capacity of 260,000 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 – 2 5,000-gallon railroad tank cars, and
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 $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?
- 3t + 27 10,000 gallon railroad tank cars will be in the fleet for a certain range of t. The
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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