Question

question
mrs. merton has decided to set up a pie making business. to set herself up in business she must purchase equipment totalling $200, plus each pie that she makes costs her 25 cents. she is planning to sell her pies for $1.50 each. if $x$ denotes the number of pies that are made, what is the correct form of the profit function $p(x)$?
select the correct answer below:
$p(x)=1.25x + 200$.
$p(x)=1.25x - 200$.
$p(x)=1.5x - 200$.
$p(x)=1.75x - 200$.

Explanation:

Step1: Calculate total cost

The fixed - cost of equipment is $200$ and the variable cost per pie is $0.25x$. So the total cost function $C(x)=200 + 0.25x$.

Step2: Calculate total revenue

She sells each pie for $1.50$, so the revenue function $R(x)=1.5x$.

Step3: Calculate profit function

Profit $P(x)=R(x)-C(x)$. Substitute $R(x)$ and $C(x)$ into the formula: $P(x)=1.5x-(200 + 0.25x)=1.5x-200 - 0.25x=1.25x - 200$.

Answer:

B. $P(x)=1.25x - 200$