43-46. Average and marginal profit 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 items is P(x)=xp(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 dp/dx. 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. a. Find the profit function P. b. Find the average profit function and the marginal profit function. c. Find the average profit and the marginal profit if x = a units are sold. d. Interpret the meaning of the values obtained in part (c). 43. C(x) =-002x² +50x+100, p(x) = 100, a = 500
43-46. Average and marginal profit 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 items is P(x)=xp(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 dp/dx. 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. a. Find the profit function P. b. Find the average profit function and the marginal profit function. c. Find the average profit and the marginal profit if x = a units are sold. d. Interpret the meaning of the values obtained in part (c). 43. C(x) =-002x² +50x+100, p(x) = 100, a = 500
Chapter3: Functions
Section3.2: Domain And Range
Problem 61SE: The cost in dollars of making x items is given by the function Cx)=10x+500. a. The fixed cost is...
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Can you answer #43?
Transcribed Image Text:43-46. Average and marginal profit 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 items is
P(x)=xp(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 dp/dx. 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.
a. Find the profit function P.
b. Find the average profit function and the marginal profit
function.
c. Find the average profit and the marginal profit if x = a
units are sold.
d. Interpret the meaning of the values obtained in part (c).
43. C(x) =-002x² +50x+100, p(x) = 100, a = 500
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