Hallo Mala,
G(x) = E(x) - K(x) = - 1/80x2 + 5x - ( 2x+100 ) = - 0.0125·x2 + 3·x - 100
a) G(x) = 0
- 0.0125·x2 + 3·x - 100 = 0
ax2 + bx + c = 0
abc-Formel: a = - 0.0125 , b = 3 , c = -100
x1,2 = ( -b ± \(\sqrt[]{b^2-4ac}\)) / (2a)
x1 = 200 (Gewinngrenze) ; x2 = 40 (Gewinschwelle)
b) G'(x) = 0 ⇔ 3 - 0.025·x = 0 ⇔ x = 120
Gruß Wolfgang