High School

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Given the cost function, [tex]C(x)[/tex], and the revenue function, [tex]R(x)[/tex], write the profit function from producing and selling [tex]x[/tex] units of the product.

[tex]
\begin{array}{l}
C(x) = 59x + 3600 \\
R(x) = 89x
\end{array}
[/tex]

A. [tex]P(x) = 30x + 3600[/tex]
B. [tex]P(x) = -30x + 3600[/tex]
C. [tex]P(x) = 30x - 3600[/tex]
D. [tex]P(x) = -30x - 3600[/tex]

Answer :

The profit function, [tex]$P(x)$[/tex], is calculated by subtracting the cost function from the revenue function. Mathematically, we write:

[tex]$$
P(x) = R(x) - C(x)
$$[/tex]

Given the revenue function

[tex]$$
R(x) = 89x
$$[/tex]

and the cost function

[tex]$$
C(x) = 59x + 3600,
$$[/tex]

we substitute these into the profit function:

[tex]$$
\begin{aligned}
P(x) &= 89x - (59x + 3600) \\
&= 89x - 59x - 3600 \\
&= (89x - 59x) - 3600 \\
&= 30x - 3600.
\end{aligned}
$$[/tex]

Thus, the profit function is

[tex]$$
P(x) = 30x - 3600.
$$[/tex]

This corresponds to option c.

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Rewritten by : Jeany

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