Given the following total revenue R(x) and total cost C(x) functions, (1) express profit as a

Given the following total revenue R(x) and total cost C(x) functions, (1) express profit π as a function of x, (2) determine the maximum level of profit by finding the vertex of π(x), and (3) find the x intercepts and draw a rough sketch of the graph.

(a)

(b)

(3) Factoring π (x) = 0 to find the x intercepts,

See Fig. 3-24.

Transcribed Image Text:

R(x) = 600x - 5.x (1) C(x) 100x + 10, 500 = (x) = R(x)-C(x) (x) = 600x-5x - (100x + 10,500) (x)=-5x+500x - 10,500 (2) Using the method of Problem 3.22, but substituting for y, x = -(500) 2(-5) x = 50 4(-5)(-10, 500) - (500)2 = 4(-5) 210,000 250,000 = 2000 -20 Maximum: (50) = 2000 Vertex: (50, 2000) (3) Factoring (x) = 0 to find the x intercepts, See Fig. 3-23. -5x+500x10,500 = 0 -5(x-100x +2100) = 0 (x 30)(x-70) = 0 - x = 30 x = 70 x intercepts: (30, 0), (70, 0)