Question

please help. Functions and Relations. What is the profit function, p(x)?

Answer 1

We need to find the profit function, P(x), defined as:

$P(x)=R(x)-C(x)$

We have:

$\begin{gathered} R(x)=-0.5x³+900x²-500x+400 \\ \\ C(x)=300x²+200x \end{gathered}$

Thus, using the above polynomial expressions in the profit definition, we obtain:

$\begin{gathered} P(x)=-0.5x³+900x²-500x+400-\left(300x²+200x\right) \\ \\ P(x)=-0.5x³+900x²-500x+400-300x²-200x \\ \\ P(x)=-0.5x³+(900-300)x²-(500+200)x+400 \\ \\ P(x)=-0.5x³+600x²-700x+400 \end{gathered}$

Answer