Using the equations R(x)=-x^2+400x and C(x)=x^2+40x+100, find the Maximum Revenue

Answer 1

P(x) = R(x) - C(x)
P(x) =-x^2 +400x -x^2 -40x -100
P(x) -2x^2 + 360x -100

P'(x) = -2x +360

solve for x
0 = -2x + 360

Answer 2

P(x) = R(x) - C(x)
P(x) =-x^2 +400x -x^2 -40x -100
P(x) -2x^2 + 360x -100

P'(x) = -4x +360

solve for x
0 = -4x + 360

R'(x ) -2x + 400
0 = -2x + 400
2x = 400
x = 200

R(200) = -(200)^2 + 400(200)
-40000 + 80000 = 40000