Formulate but do not solve the problem The management of Har

Formulate but do not solve the problem. The management of Hartman Rent-A-Car has allocated $2.16 million to buy a fleet of new automobiles consisting of compact, intermediate-size, and full-size cars. Compacts cost $18,000 each, intermediate-size cars cost $27,000 each, and full-size cars cost $36,000 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.)

________= 2,160,000

________= x

________= 100

Solution

Solution: - Let x,y,z denote the number of compact, intermediate sized, and full size cars purchased respectively.

18000 x + 27000 y + 36000 z = 2160000........(1)

2y = x.......(2)

x + y +z = 100 ......(3)

Plug x =2y in equation (1) and equation (2) to solve the problem