Question

The profit P(x) of a company is modeled by the quadratic function P(x)=−2x2+40x−100, where x is the number of items sold. What is the profit when 5 items are sold? Find P(5).

Answer 1

To find the profit when 5 items are sold, we need to evaluate the function \( P(x) \) at \( x = 5 \).

The profit function is given by:

\[
P(x) = -2x^2 + 40x - 100
\]

Now, we will substitute \( x = 5 \) into the equation:

\[
P(5) = -2(5)^2 + 40(5) - 100
\]

Calculating \( (5)^2 \):

\[
(5)^2 = 25
\]

Now substituting back into the equation:

\[
P(5) = -2(25) + 40(5) - 100
\]

Calculating \( -2(25) \):

\[
-2(25) = -50
\]

Calculating \( 40(5) \):

\[
40(5) = 200
\]

Now substituting these values back into the equation:

\[
P(5) = -50 + 200 - 100
\]

Combining these values:

\[
P(5) = 150 - 100 = 50
\]

Thus, the profit when 5 items are sold is

\[
\boxed{50}
\]