Kevin is an auto mechanic. He spends 2 hours when he replaces the shocks on a car and 2 hours when he replaces the brakes. He works no more than 42 hours a week. He routinely completes at least 2 shocks replacements and 6 brake replacements a week. If he charges ?$500 for labor replacing shocks and ?$250 in labor for replacing? brakes, how many jobs of each type should he complete a week to maximize his? income?

Let X be number of jobs for replacement of Shocks

Let Y be number of Jobs for replacement of Brakes

Below are the equations based upon available information

2X + 2Y <= 42 hrs

X >= 2

Y >= 6

By plotting above equations on graph(see attached) we get following corner points of bounded region.

A(2,19), B(2,6), C(15,6)

we need to maximize R = 500X + 250Y

Value of R at point A = 500*2 + 250*19 = 5750

Value of R at point B = 500*2 + 250*6 = 2500

Value of R at point C = 500*15 + 250*6 = 9000

As the value of R is maximum at point C. Hence he should have 15 jobs for repair of Shocks and 6 jobs for repair of Brakes to get maximum income of $9000 per week

please see the attached file for the complete solution.