Whittaker Donnelly

11/23/2023 · Senior High School

Let \( C(x) \) represent the cost of producing \( x \) items and \( p(x) \) be the sale price per item if \( x \) items are sold. The proft \( P(x) \) of selling \( x \) items is \( P(x)=x p(x)-C(x) \) (revenue minus costs). The average profit per item when \( x \) items are sold is \( P(x) / x \) and the marginal profit is \( d P / d x \). The marginal profit approximates the profit obtained by selling one more item given that \( x \) items have already been sold. Consider the following cost functions \( C \) and price functions \( p \). Complete parts (a) through (d) below \( C(x)=-003 x^{2}+60 x+120 \quad P(x)=200 \quad a=500 \) a. Find the profit function \( P \) The profit function is \( P(x)=\square \)