Find the break-even point for the firms with the following linear total revenue R(x) and total cost C(x) functions by (1) finding the profit π(x) function, setting it equal to zero, and solving for x, (2)

setting R(x) = C(x) and solving for x, and (3) graphing R(x) and C(x) and finding the point of intersection.

(a)

(b)

(2) Setting R(x) = C(x) and solving for x,

(3) See Fig. 4-19.

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R(x): = 55x C(x) = 30x + 250 (1) Finding the profit function (x), == (x) = R(x)-C(x) = 55x (30x +250) = 25x250 Setting it equal to zero and solving for x, 25x-250=0 - x = 10 Break-even level of output (2) Setting R(x)=C(x) and solving for x, 55x30x+250 25x = 250 x = 10 Break-even level of output (3) See Fig. 4-18.