## Question

###### Let C(x) 5 represent the cost of producing items and p(x) be the sale price per item if x items are sold. The profit P(x) of selling items is P(x) =xp(x) - C(x) (revenue minus costs). The average profit per item when items are sold is P(x) /x and the margina profit is dP / dx The marginal profit approximates the profit obtained by selling one more item given that items have already been sold_ Consider the following cost functions and price functions Complete parts (a) through (d) below:c(x) = 0

Let C(x) 5 represent the cost of producing items and p(x) be the sale price per item if x items are sold. The profit P(x) of selling items is P(x) =xp(x) - C(x) (revenue minus costs). The average profit per item when items are sold is P(x) /x and the margina profit is dP / dx The marginal profit approximates the profit obtained by selling one more item given that items have already been sold_ Consider the following cost functions and price functions Complete parts (a) through (d) below: c(x) = 0.02x2 40x + 100 , p(x): 300 , 500 Find the profit function The profit function P(x) = 0.02x2_ 260x - 100 Find the average profit function and margina profit function_ Plx) The average profit function is

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