a)
K(x) = 0.0001·x^3 - 0.03·x^2 + 100·x + 170000
K(200) = 189600 €
b)
p(0) = 10300 €
p(x) = 0
0.0001·x^2 - 85.03·x + 10300 = 0 --> x = 121 Stück
c)
K(x) = a·x^3 + b·x^2 + c·x + d
K''(30) = 0
K(30) = 4788
K'(x) = 1.2
K(70) = 70·70
Die Lösung ist: a = 0.001 ∧ b = -0.09 ∧ c = 3.9 ∧ d = 4725
K(x) = 0.001·x^3 - 0.09·x^2 + 3.9·x + 4725
d)
k(x) = (0.001·x^3 - 0.09·x^2 + 3.9·x + 4725)/x = 0.001·x^2 - 0.09·x + 4725/x + 3.9
k'(x) = 0.002·x - 4725/x^2 - 0.09 = 0 --> x = 150 Stück.