Give the following revenue and cost functions, find the break even point (equilibrium point)
R(x)= 56x-2x^2; C(x)=24x+101
The X^2 is the only thing that throws me off. Im not sure what im doing.
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The equilibrium point x= a is the point where,
R(x) = C(x) at x=a or
So,solving for x, when 56x-2x^2=24x+101 or
2x^2+24x-56x+101 = 0, we get a.
2x^2-32x+101 = 0 or
2(x-8)^2-2*8^2+101 =0 or
2(x-8)^2 = 128-101 = 27 or
(x-8)^2 = 27/2 =13.5. or
x=8+sqrt13.5=11.6742 is the break even point where R(11.6742) and C(11.6742) equal and there is no profit and no loss.
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