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 function p. c(x)=-0.02x^2+40x+80, p(x)=100, a=500a) what is the profit function p. p(x)=? b) find the average profit function and marginal profit function. average profit function: p(x)/(x)=? marginal profit function: dp/dx=? c

(a) Profit function P(x) = 0.02x^2+60x-80

(b) Average profit P(x)/x = P/x = 0.02x+60-80/x

Marginal profit dP/dx = 0.04x+60

Step-by-step explanation:

Cost function: C(x) = -0.02x^2+40x+80

Price function: p(x) = 100

(a) The profit function P(x) = x*p(x)-C(x) can be expressed as:

(b)Average profit function: P(x)/x

Marginal profit function: dP/dx

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step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

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