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 4 shocks replacements and 6 break replacements a week. If he charges $450 for labor replacing shock and $200 in labor for replacing breaks, 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 should do 15 shock replacements and 6 brake replacements every week to maximize his weekly income.

Step-by-step explanation:

Both jobs take the same amount of time to complete (2 hours), therefore, in order to maximize his income, Kevin should prioritize the job that gives him the greatest income, which is replacing shocks.

If each job takes 2 hours and he works at most 42 hours per week, Kevin can complete 21 jobs per week. He should aim to do as little break replacements as possible and as many shock replacements as possible to maximize income.

If he completes at least 6 break replacements, the remaining jobs should all be shock replacements:

Kevin should do 15 shock replacements and 6 brake replacements every week to maximize his weekly income.

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