Question

Jimmy decides to mow lawns to earn money. The initial cost of his lawnmower is %350. Gasoline and maintenance costs a $6 per lawn. 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? a) Formulate a function C(x) for the total cost of mowing x lawns. b) Find a function for the total revenue from mowing x lawns R(x) = How much does Jimmy charge per lawn?

Answer 1

Answer:

Step-by-step explanation:

Answer 2

a) C(x) = 6x+350

b) Function for total revenue, R(x) = 15x & charge per lawn is $15.

c) Jimmy must mow approx 39 lawns before he begins making a profit.

How to formulate a function ?

Consider the initial cost of lawnmower is $350,

Gasoline and maintenance cost are $6 per lawn.

(a) To formulate a function C(x) for the total revenue of mowing x lawn, we use the given values than the function C(x) will be given by

C(x) = 6x+350

How to find the total revenue ?

Find the function for the total revenue from moving x lawns.

Recollect: P(x) = R(x)-C(x)

So, R(x) = P(x)+C(x)  ..............(1)

Substitute, P(x) = 9x-350 & C(x) = 6x+350 in (1) we get,

R(x) = 9x-350+6x+350

      = 15x

So, the total revenue = 15x

∴ Charge per lawn = R(x)/x = 15x/x = $15

How much lawn jimmy needs to mow before make profit ?

To find the number of lawn jimmy must mow before begins making a profit, we use P(x) = 0

∴ 9x-350=0

⇒x = 350/9

⇒x ≈ 39

Hence, the solution is x = 39 (approx)

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