Melissa runs a landscaping business. She has equipment and fuel expenses of $264 per month. If she c

Melissa runs a landscaping business. She has equipment and fuel expenses of $264 per month. If she charges $53 for each lawn, how many lawns must she service to make a profit of at $800 a month?

Melissa has a fixed cost of $264 per month in fuel. No variable cost is given. Our cost function is:
C(x) = Fixed Cost + Variable Cost. With variable cost of 0, we have:
C(x) = 264

The revenue per lawn is 53. So R(x) = 53x where x is the number of lawns.

Now, profit is Revenue - Cost. Our profit function is:
P(x) = 53x - 264

To make a profit of $800 per month, we set P(x) = 800.
53x - 264 = 800

Using our equation solver, we get:
x ~ 21 lawns