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

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²

↓↓↓↓↓↓↓↓↓

step-by-step explanation:

this is a parabola.