Kevin is an auto mechanic. He spends 3 hours when he replaces the shocks on a ca

Question

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. If he charges $500 for labor replacing shocks and $300 in labor for replacing brakes, how many jobs of each type should he complete a week to maximize his income? Kevin should doshock replacements and brake replacements every week to maximize his weekly incoma.

Explanation / Answer

Let Kevin replace x shocks and y brakes per week. Then, x ? 4 and y ? 6. Also, the no. of hours spent on replacing the shocks and the brakes are 3x and 2y respectively so that 3x+2 = 48. Further, Kevin’s weekly income is I(x,y) = 500x+300y . Apparently, to maximize his income, Kevin should maximize x and minimize y. Now, since the minimum value of y is 6, hence for maximum income, we have 3x+2*6 = 48 or, 3x= 48-12 = 36. Then x = 36/3 = 12. Thus, to maximize his income, Kevin should do 12 shock replacements and 6 brake replacements.

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