Logan Herrera

11/13/2023 · 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 profit \( P(x) \) of selling \( x \) iterns 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 seling one more item given that \( x \) iterns have already been sold. Consider the following cost functions \( C \) and price functions \( p \). Complete parts (a) through ( \( d \) ) below \( C(x)=-0.03 x^{2}+60 x+120, p(x)=200 a=500 \) d. Interpret the meaning of the values obtained in part (c). Interpret the average profit if \( x= \) a units have been sold Choose the correct answer below A The average profit per item for each of the first 500 iterts produced is \( \$ 15476 \) B. The profit for the 170 items produced is \( \$ 50000 \) C. The profit for the 501 st item produced is \( \$ 17000 \) D. The average prafit for the first 500 items produced is \( \$ 154.76 \)