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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 54 hours a week. He routinely completes at least 4 shocks replacements and 6 brake replacements a week. If he charges $450 for labor replacing shocks and $200 in labor for replacing 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

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Answer:

Kevin should do 21 shock replacements and 6 brake replacements every week to maximize his weekly income.

Step-by-step explanation:

Since either job takes 2 hours to complete, the total number of jobs that Kevin can complete working 54 hours a week is:

[tex]n=\frac{54}{2}\\n=27\ jobs[/tex]

Since replacing shocks gives him a greater income, he should aim to do as little break replacements as possible and as many shock replacements as possible in order to maximize income.

If he has to complete at least 6 break replacements out of the 27 jobs possible, the number of shock replacements he should do is:

[tex]S=27-6\\S=21[/tex]

Kevin should do 21 shock replacements and 6 brake replacements every week to maximize his weekly income.

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