Math  /  Algebra

QuestionA chemical manufacturer wants to lease a fleet of 26 railroad tank cars with a combined carrying capacity of 392,000 gallons. Tank cars with three different carrying capacities are available: 7,000 gallons, 14,000 gallons, and 28,000 gallons. Letting t=t= number of 28,000 railroad tank cars in the fleet, 2t47,0002 t-47,000-gallon railroad tank cars, and 3t+30-3 \mathrm{t}+30 14,000 gallon railroad tank cars will be in the fleet for a certain range of tt. The cost of leasing a 7,000 -gallon tank car is $550\$ 550 per month, a 14,000 -gallon tank car is $750\$ 750 per month and a 28,000 -gallon tank car is $1350\$ 1350 per month. Which of the solutions to the number of each type of tank car in the fleet would minimize the monthly leasing cost? \square \square 7,000-gallon tank cars, 14,000-gallon tank cars, and \square 28,000-gallon tank cars. (Simplify your answers. Type whole numbers.)

Studdy Solution
Calculate numbers of each tank:
{7,000 gallon cars: 2(7)47=1447=3314,000 gallon cars: 3(7)+30=21+30=928,000 gallon cars: 7\begin{cases} 7,000 \text{ gallon cars: } 2(7) - 47 = 14-47 = -33 \\ 14,000 \text{ gallon cars: } -3(7) + 30 = -21+30 = 9\\ 28,000 \text{ gallon cars: } 7 \\ \end{cases}
\text{Confirm all constraints met.}

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