An accountant is identifying the profits for a company. The company’s revenues are represented by the function R(x)=30x+155

Question

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 point)
Responses

P(x)=17x+153
upper P left parenthesis x right parenthesis equals 17 x plus 153

P(x)=−17x−153
upper P left parenthesis x right parenthesis equals negative 17 x minus 153

P(x)=43x+153
upper P left parenthesis x right parenthesis equals 43 x plus 153

P(x)=17x+157
upper P left parenthesis x right parenthesis equals 17 x plus 157

Answer 1

To find the profit function \( P(x) \), we subtract the cost function \( C(x) \) from the revenue function \( R(x) \).

Given:

• Revenue function: \( R(x) = 30x + 155 \)
• Cost function: \( C(x) = 13x + 2 \)

The profit function can be calculated as follows:

\[ P(x) = R(x) - C(x) \] Substituting the given functions:

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

Now, distribute the negative sign in the cost function:

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

Combine like terms:

\[ P(x) = (30x - 13x) + (155 - 2) \] \[ P(x) = 17x + 153 \]

Therefore, the profit function is:

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

Thus, the correct answer is:

P(x) = 17x + 153