Question

The cost of producing x soccer balls in thousands of dollars is represented by h(x) = 5x + 6. The revenue is represented by k(x) = 9x – 2. Which expression represents the profit, (k – h)(x), of producing soccer balls?
14x – 8
14x + 4
4x – 8
4x + 4

Answer 1

To find the profit function, we need to subtract the cost function \( h(x) \) from the revenue function \( k(x) \). The profit is given by:

\[
P(x) = k(x) - h(x)
\]

Given the functions:
- Cost function: \( h(x) = 5x + 6 \)
- Revenue function: \( k(x) = 9x - 2 \)

We can substitute these functions into the profit equation:

\[
P(x) = (9x - 2) - (5x + 6)
\]

Now, simplify the expression:

\[
P(x) = 9x - 2 - 5x - 6
\]

Combining like terms:

\[
P(x) = (9x - 5x) + (-2 - 6)
\]
\[
P(x) = 4x - 8
\]

So, the expression that represents the profit \( (k - h)(x) \) is:

\[
\boxed{4x - 8}
\]