Kathleen is a high school student who has been investigating the possibility of mowing lawns for a summer job. She has a few friends she could hire on an hourly basis. The equipment would cost her $500, and she estimates her cost per lawn would be $14, based on the time required to pay her friends (not including her own labor) and gasoline for driving to the jobs and for the mowers. Kathleen has eight weeks available to mow lawns before school starts again, and she estimates that she can get enough customers to mow at least three lawns per day, six days per week. How much profit can she expect to make over the summer in dollars?

She must pay $500 for the materials, and $14 per lawn, then:

We know that the total cost is (assuming that they work for 8 weeks, 6 days per week, and 3 times per day)

C = $500 + $14*(8*6*3) = $2,516.

The total revenue that she can make (with the same assumptions as before) is:

R = N*(8*6*3)

Where N is the amount she charges for each lawn that they mowed.

R = N*144

Now, we do not know how much she charges, so the value of N is unknown.

Now, the profit is equal to the difference between the revenue and the cost, this means that the profit is:

P = R - C = N*144 - ($2,516)

P(N) = N*144 - ($2,516)

If we have, for example, N = $20, the total profit will be:

P($20) = $20*144 - ($2,516) = $364

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