A chemical manufacturer wants to lease a fleet of 23 railroad tank cars with a c

Question

A chemical manufacturer wants to lease a fleet of 23 railroad tank cars with a combined carrying capacity of 350,000 gallons. Tank cars with three different carrying capacities are available: 7,000 gallons, 14,000 gallons, and 28,000 s. Letting t -number of 28,000 railroad tank cars in the fleet, 2t -4 7,000-gallon railroad tank cars, and - 3t27 14,000 gallon railroad tank cars will be in the fleet for a certain range of t. The cost of leasing a 7,000-gallon tank car is $250 per month, a 14,000-gallon tank car is $750 per month, and a 28,000-gallon tank car is $1050 per month. Which of the solutions to the number of each type of tank car in the fleet would minimize the monthly leasing cost? 7.000-gallon tank cars, 14,000-gallon tank cars, and 28,000-gallon tank cars. (Simplify your answers. Type whole numbers.)

Explanation / Answer

Variable

t = number of 28000 tank cars

Constrains

1. t is integer and non-negative

2. 28000t + 14000 (-3t+27) + 7000 (2t-4) >= 350,000

Objective

Minimize the cost = 1050t + 750 (-3t+27) + 250 (2t-4)

Solution

so answer is 28000 gallon car are to be taken 9 and 7000 gallon car to be taken 14

Per car total Car number capacity cost capacity cost 7000 gallon 14 7000 250 98000 3500 14000 gallon 0 14000 750 0 0 28000 gallon 9 28000 1050 252000 9450 total 350000 12950 constraint 0

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