Find the break-even point for the firms with the following quadratic total revenue R(x) functions by

(1) finding the profit π(x) function, setting it equal to zero, and solving for the x’s; (2) setting R(x) =

C(x) and solving for the x’s; and (3) graphing R(x) and C(x) and finding the point of intersection.

(a)

(3) Using the techniques of Section 3.6 to graph the quadratic function R(x) = −4x2 + 72x, (i) With a = −4

The x intercepts are (0, 0) and (18, 0). See Fig. 4-20 for the graphs of R(x) and C(x) and the points of intersection.

(b)

(3) Graphing R(x) = −5x2 + 750x, as above,

The x intercepts are (0, 0) and (150, 0). See Fig. 4-21.

Transcribed Image Text:

R(x)=-4x + 72x C(x)=16x + 180 (1) (x)=-4x + 72x (16x + 180) = -4x + 56x-180 Setting (x)=0 and factoring, -4x+56x180 = 0 -4(x-14x+45) = 0 (x-5)(x-9) = 0 x = 5 x=9 Break-even levels of output (2) Setting R(x) = C(x), Then factoring as in (1), -4x+72x=16x + 180 -4x+56x180 = 0 x = 5 x = 9 Break-even levels of output