Question

A company has found that the relationship between the price p and thePdemand x for a particular product is given approximately byp= 1115 – 0.09x2.The company also knows that the cost of producing the product is given byC(x) = 840 + 385x.Find P(x), the profit function.

Answer 1

The profit is computed as follows:

Profit = price - cost

Substituting with:

$\begin{gathered} \text{price}=p(x)=1115-0.09x^2 \\ \text{ cost =c}(x)=840+385x \end{gathered}$

we get:

$\begin{gathered} P(x)=p(x)-c(x) \\ P(x)=1115-0.09x^2-(840+385x) \\ \text{Combining similar terms:} \\ P(x)=1115-0.09x^2-840-385x \\ P(x)=-0.09x^2-385x+1115-840 \\ P(x)=-0.09x^2-385x+275 \end{gathered}$