Question

Sue is starring a lawn-cutting business. Her start-up cost tot buy two lawn mowers and an edge trimmer is $665. She has figured out that she will use

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asked 2021-06-29
Sue is starring a lawn-cutting business. Her start-up cost tot buy two lawn mowers and an edge trimmer is $665. She has figured out that she will use about $1 in gas for each lawn. If she charges $20 per lawn what will her break-even point be?

Answers (1)

2021-06-30

The break-even point occurs when the total cost is equal to the total revenue.
If xx is the number of lawns, then the total cost of Sue is the sum of $665 and the cost in gas per lawn times the number of lawns:
\(P(x)=665+1(x)\)
\(P(x)=665+x\)
and her revenue is the amount she charges times the number of lawns:
\(R(x)=20x\)
So, we equate and solve for x:
\(P(x)=R(x)\)
\(665+x=20x\)
\(665=19x\)
\(35=x\)
Solve for the cost using either P or R:
\(R(35)=20(35)=700\)
The break-even point is (35,700) which means that the cost and revenue are equal for 35 lawns at $700.

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