Question

Jimmy decides to mow lawns to earn money. The initial cost of his electric lawnmower is ​$350. Electricity and maintenance costs are ​$4 per lawn. Complete parts​ (a) through​ (c).a. Formulate a function C(x) for the total cost of mowing x lawns. 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 lawns. How much does jimmy charge per lawn? c. How many lawns must jimmy mow before he begins making a profit?

Answer 1

Answer:

a) C(x) = 4x + 350

b) 13x; $13

c) 39

Step-by-step explanation:

a) Initial cost of lawnmower = $350

Maintenance cost for 1 lawn = $4

Maintenance cost for x lawns = 4x

Total cost function, C(x) = 4x + 350

b) Revenue = Cost + Profit

= C(x) + P(x)

= 4x + 350 + 9x - 350

= 13x

Charge per lawn = $\frac{\text{Revenue}}{\text{Number of lawns}}$

= $\frac{13x}{13} = \ 13$

c) For Jimmy to make a profit, P(x) must be greater than zero i.e.

$P(x) >0$

$9x-350 >0$

$9x >350$

The smallest integer value of x that satisfies this inequality is 39. Therefore, Jimmy needs to mow 39 lawns in order to start making profit.