Question

the linear profit function is $p(x) = 30x - 650$.
(d) determine the number of lawn maintenance calls needed per month for the company to make money. round up your answer to the nearest. the business will make a profit if 22 or more lawn maintenance calls are made per month.
(e) if 41 maintenance calls are made for a given month, how much money will the lawn service make or lose? write your answer to the nearest cent. if 41 maintenance calls are made for a given month the business will make

Explanation:

Step1: Solve for profit (Part d)

Set $P(x) > 0$, so $30x - 650 > 0$

Step2: Isolate x (Part d)

$30x > 650 \implies x > \frac{650}{30} \approx 21.67$

Step3: Round up to integer (Part d)

Since calls are whole numbers, $x=22$

Step4: Calculate profit for x=41 (Part e)

Substitute $x=41$ into $P(x)=30x-650$

Step5: Compute the value (Part e)

$P(41)=30(41)-650=1230-650=580$

Answer:

(d) 22
(e) The business will make $\$580.00$