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 $180 for 3,000 cubic feet, $225 for 4,500 cubic feet, and $325 for 6,000 cubic feet. Which of the solutions in part (A) would minimize the monthly leasing costs?