The cost of producing x units of balloons is given by C(x) =140 + 0.125x + 0.0005x^2. If the revenue function is determined by R(x) = 3x, maximum profit is:

Answer 1

it occurs where d/dx(R-C) = 0

I get a maximum profit of 3992.81 at x=2875

Answer 2

profit=Revenue-cost

R=3x
d/dx = 3

C=140+0.125x+0.0005x^2
d/dx=0.001X+0.125

profit=Revenue-cost
p= 3-( 0.001X + 0.125)
p=3 - 0.001x - 0.125
3 - 0.001x - 0.125=0
x=2875

p(x)=R(x)-C(x)
P(2875)= (3x) - (140+0.125x+0.0005x^2)
P(2875)= 3x - 140 - 0.125(2875) - 0.0005(2875)^2
P(2875)=3992.81