Question

What’s the answer to this a) [in the picture]b) Jimmy determines that the total profit function for the lawn mowing business is given by P(x)=9x-350 find a function for the total revenue from mowing X lawnsc) How much does Jim Jimmy charge per lawn? how many lawns much Jimmy mow before he begins making a profit?

Answer 1

a) The total cost can be expressed as the sum of a fixed cost, which is the initial cost of $350, and a variable cost, which is $5 per lawn.

Then, we can write the total cost C(x) as:

`C(x)=350+5x`

b) We know that the profit function is P(x) = 9x - 350.

We have to find the revenue function R(x).

We know that the profit function P(x) is equal to the revenue R(x) minus the cost C(x), so we can write:

`\begin{gathered} P(x)=R(x)-C(x) \\ 9x-350=R(x)-(350+5x) \\ 9x-350=R(x)-350-5x \\ 9x+5x-350+350=R(x) \\ 14x=R(x) \\ \Rightarrow R(x)=14x \end{gathered}`

c) We see from the revenue function R(x) = 14x that he charges $14 per lawn.

We can calculate how many lawns (x) he has to mow in order to make a profit.

This can be calculated as the x that makes P(x) = 0:

`\begin{gathered} P(x)=0 \\ 9x-350=0 \\ 9x=350 \\ x=(350)/(9) \\ x\approx38.88 \\ x\approx39 \end{gathered}`

He will make a profit after mowing 39 lawns.

Answer: a) the total cost is C(x) = 350 + 5x.

b) the revenue function is R(x) = 14x.

c) he charges $14 per lawn. He need