The total cost and the total revenue (in dollars) for the production and sale of

Question

The total cost and the total revenue (in dollars) for the production and sale of x ski jackets are given by C(x) = 28x + 20,160 and R(x) = 200x - 0.2x2 for 0 x 1000. Find the value of x where the graph of R(x) has a horizontal tangent line. Find the profit function P(x). Find the value of x where the graph of P(x) has a horizontal tangent line. Graph C(x), R(x), and P(x) on the same coordinate system for 0 x 1000. Find the break-even points. Find the x intercepts of the graph of P(x). R(x) has a horizontal tangent line at x = 500 . The profit function P(x) =

Explanation / Answer

A. find the graph of function where graph has tanget line

tangent line means slope is zero

thus

slope dR/dx = 0

dR/dx = 0

200-0.4x = 0

x = 500

B. Profit function

P = R(x) - C(x) = 200x - 0.2x^2 -28x-20160 =

P(x) = -0.2x^2 + 172x - 20,160

C. find the graph of function where graph has tanget line

tangent line means slope is zero

thus

dP/dx = 0

200-0.4x-28 =0

x = 430

D.

Break even points are when C = R

28x+20160= 200x-0.2x^2

x = 720 or 140

x intercepts of P(x)

put y = 0

thus

-0.2x^2 + 172x - 20,160 = 0

{x=720, x=140}

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