Kevin is an auto mechanic. He spends 3 hours when he replaces the shocks on a car and 2 hours when he replaces the brakes. He works no more than 54 hours a week.He routinely completes at least 4 shocks replacements and 6 brake replacements a week. If he charges $400 for labor replacing shocks and $200 in labor forreplacing brakes, how many jobs of each type should he complete a week to maximize his income?Kevin should do shock replacements and brake replacements every week to maximize his weekly income.

Kevin is an auto mechanic. He spends 3 hours when he replaces the shocks on a car and 2 hours when he replaces the brakes. He works no more than 48 hours a week. He routinely completes at least 4 shocks replacements and 6 brake replacements a week. He charges $500 for labor replacing shocks and $300 in labor for replacing brakes. We have to find how many jobs of each type should he complete a week to maximize his income.Let x be the number of replaced shocks and y be the number of replaced brakes. Kevin spends 3 hours when he replaces the shocks on a car and 2 hours when he replaces the brakes. He works no more than 48 hours a week. 3x+2y≤48 He routinely completes at least 4 shocks replacements and 6 brake replacements a week. x≥4y≥6 He charges $500 for labor replacing shocks and $300 in labor for replacing brakes. The objective function becomes z=500x+300y. The linear programming model, max z=500x+300y Subject to the constraints, 3x+2y≤48x≥4y≥6x,y≥0.Use the graphical method to solve the LPP, Consider the constraint, 3x+2y=48 x 0 16 y 24 0 Graph of the feasible region: The corner points are 4, 6, 4, 18, and 12, 6.Find the objective function value at the corner points: Corner points Objective function value 4, 6 z=5004+3006=3800 4, 18 z=5004+30018=7400 12, 6 z=50012+3006=7800 The maximum value is 7800, it occurs at 12, 6.Final answer: Kevin should do 12 shock replacements and 6 brake replacements every week to maximize his weekly income.