Question

An accountant is identifying the profits for a company. The company's revenues are represented by the function R(x)+30x+155 and the costs by C(x)=13x+2, where x is the number of units sold. Build a profit function. (Hint: Profit can be found by subtracting cost from the revenue.)
1)P(x)=17x+157
2)P(x)=-17x-153
3)P(x)=43x+153
4)P(x)=17x+153

Answer 1

To find the profit function \( P(x) \), we can use the formula:

\[
P(x) = R(x) - C(x)
\]

Given that the revenues are represented by the function:

\[
R(x) = 30x + 155
\]

and the costs are represented by the function:

\[
C(x) = 13x + 2,
\]

we can substitute these into the profit function:

\[
P(x) = (30x + 155) - (13x + 2).
\]

Now, let's simplify this expression:

1. Distribute the negative sign through the costs \( C(x) \):

\[
P(x) = 30x + 155 - 13x - 2.
\]

2. Combine like terms:

\[
P(x) = (30x - 13x) + (155 - 2).
\]

This simplifies to:

\[
P(x) = 17x + 153.
\]

Thus, the profit function is:

\[
P(x) = 17x + 153.
\]

Based on the options provided, the correct answer is:

4) \( P(x) = 17x + 153 \).