Chapter 4, Problem 43RE

Business leases. A grain company wants to lease a fleet of $20$ covered hopper railcars with a combined capacity of $108,000$ cubic feet. Hoppers with three different carrying capacities are available: $3,000$ cubic feet. $4,500$ cubic feet, and $6,000$ cubic feet.

(A) How many of each type of hopper should they lease?

(B) The monthly rates for leasing these hoppers are $\text{\$180}$ for $3,000$ cubic feet, $\text{\$225}$ for $4,500$ cubic feet, and $\text{\$325}$ for $6,000$ cubic feet. Which of the solutions in part (A) would minimize the monthly leasing costs?