Question

question
a sportswear manufacturer is introducing a new line of sneakers. to introduce the new line, the company must pay out a fixed cost of $1.5m for advertising and equipment, plus there is a cost of 40 cents per pair of sneakers manufactured. it plans to sell the sneakers for $75 per pair. what is the correct form of the profit function $p(x)$, where $x$ is the number of pairs of sneakers manufactured?
select the correct answer below:
$p = 74.6x - 1,500,000$.
$p = 75x - 1,500,000$.
$p = 75x + 1,500,000$.
$p = 74.6x + 1,500,000$.

Explanation:

Step1: Calculate total cost

The fixed - cost is $1.5m = 1500000$ dollars and the variable cost is $0.4x$ dollars (since 40 cents = $0.4$ dollars per pair and $x$ is the number of pairs). So the total cost $C(x)=1500000 + 0.4x$.

Step2: Calculate total revenue

The selling price per pair is $75$ dollars, so the total revenue $R(x)=75x$.

Step3: Calculate profit function

Profit $P(x)=R(x)-C(x)$. Substitute $R(x)$ and $C(x)$: $P(x)=75x-(1500000 + 0.4x)=75x-1500000 - 0.4x=74.6x-1500000$.

Answer:

A. $P = 74.6x - 1,500,000$