Given:
The revenue function is
[tex]R(x)=126.98x-0.5x^2[/tex]
The cost function is
[tex]C(x)=3809.40+0.7x^2[/tex]
To find:
The profit function.
Solution:
We know that, the total profit P is defined as total revenue R minus total cost C.
So, the profit function is
[tex]P(x)=R(x)-C(x)[/tex]
[tex]P(x)=126.98x-0.5x^2-(3809.40+0.7x^2)[/tex]
[tex]P(x)=126.98x-0.5x^2-3809.40-0.7x^2[/tex]
[tex]P(x)=-3682.42-1.2x^2[/tex]
Therefore, the profit function is [tex]P(x)=-3682.42-1.2x^2[/tex].
