Question

Formulate but do not solve the problem.

The management of Hartman Rent-A-Car has allocated $2.24 million to buy a fleet of new automobiles consisting of compact, intermediate-size, and full-size cars. Compacts cost $16,000 each, intermediate-size cars cost $24,000 each, and full-size cars cost $32,000 each. If Hartman purchases twice as many compacts as intermediate-size cars and the total number of cars to be purchased is 100, determine how many cars of each type will be purchased. (Assume that the entire budget will be used. Let x, y, and z denote the number of compact, intermediate-sized, and full-size cars purchased, respectively.)

Answer 1

Let number of compact sized car is = x

Number of intermediate car is = y

Number of large size car is = z

Cost of compact sized car is = $16000

So cost of x number of compact size car is = 16000x

Cost of intermediate size car is = $24000

So cost of y number of intermediate size car is = 24000y

Cost of full size car is = $32000

So cost of z number of full size car is = 32000z

Total cost is $2.24 million = 2240000

So we can write

...........................................(i)

As company purchased twice as many as compact as intermediate sized cars.

So we can write

.........................................(ii)

Total number of car purchased = 100

.....................................(iii)

So we have three equations as: