A chemical manufacturer wants to lease a fleet of 24 railroad tank cars with a combined carrying capacity of 520,000 gallons. Tank cars with three different carrying capacity are available: 8,000 gallons, 16,000 gallons, and 24,000 gallons.

(a) show the linear system of equations in terms of x,y, and z; x,y, and z being the number of tank-cars with carrying capacities of 8,000, 16,000, and 24,000 gallons respectively.

(b) solve the system of equations.

(c) If the cost of leasing an 8,000 gallon tank car is $450 per month, a 16,000 gallon tank car is $650 per month, and a 24,000 gallon tank car is $1,150 per month, then which of the solutions would minimize the monthly leasing cost?