A chemical manufacturer wants to lease a fleet of 29 railroad tank cars with a combined carrying capacity of 552,000 gallons. Tank cars with three different carrying capacities are available: 6,000 gallons, 12,000 gallons, and 24,000 gallons. Letting t= number of 24,000 railroad tank cars in the fleet, 2t-34 6,000-gallon railroad tank cars, and -3t+63 12,000 gallon railroad tank cars will be in the fleet for a certain range of t. The cost of leasing a 6,000-gallon tank car is $350 per month, a 12,000-gallon tank car is $750 per month, and a 24,000-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? 6,000-gallon tank cars, 12,000-gallon tank cars, and 24,000-gallon tank cars. (Simplify your answers. Type whole numbers.)
A chemical manufacturer wants to lease a fleet of 29 railroad tank cars with a combined carrying capacity of 552,000 gallons. Tank cars with three different carrying capacities are available: 6,000 gallons, 12,000 gallons, and 24,000 gallons. Letting t= number of 24,000 railroad tank cars in the fleet, 2t-34 6,000-gallon railroad tank cars, and -3t+63 12,000 gallon railroad tank cars will be in the fleet for a certain range of t. The cost of leasing a 6,000-gallon tank car is $350 per month, a 12,000-gallon tank car is $750 per month, and a 24,000-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? 6,000-gallon tank cars, 12,000-gallon tank cars, and 24,000-gallon tank cars. (Simplify your answers. Type whole numbers.)
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A chemical manufacturer wants to lease a fleet of 29 railroad tank cars with a combined carrying capacity of 552,000 gallons. Tank cars with three
different carrying capacities are available: 6,000 gallons, 12,000 gallons, and 24,000 gallons. Letting t= number of 24,000 railroad tank cars in the fleet,
2t - 34 6.000-gallon railroad tank cars, and -3t+63 12,000 gallon railroad tank cars will be in the fleet for a certain range of t. The cost of leasing a
6,000-gallon tank car is $350 per month, a 12,000-gallon tank car is $750 per month, and a 24,000-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?
6,000-gallon tank cars, 12,000-gallon tank cars, and 24,000-gallon tank cars.
(Simplify your answers. Type whole numbers.)
Expert Solution
Step 1
Given :-
A chemical manufacturer wants to lease a fleet of railroad tank cars with a combined carrying capacity of gallons. Tank cars with three different capacities are available : gallons , gallons , and gallons. Letting number of gallons rail road tank cars in the fleet , gallons railroad tank cars and , gallons railroad tank cars will be in the fleet for a certain range of . The cost of leasing a gallons tank car is per month , a gallons tank cars is per month , gallons tank cars is per month.
To Determine :-
The solutions to the number of each type of tank car in the fleet would minimize the monthly leasing cost.
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