k_{v}(x)

N(x_{min},0)

T(x_{opt},LPU)

H(x_{xopt},0)

x_u

x_o

K(x)

K(x)=

K(x)

P(x)

P(x)=

P(x)

E(x)

E(x)

G(x)

G(x)

K'(x)

K'(x)

G'(x)

G'(x)

G''(x)

G''(x)

K''(x)

K''(x)

k(x)

k(x)

k'(x)

k'(x)

k_v(x)

k_{v}'(x)

k_v'(x)

T_1(x_{min},KPU)

Wendepunkt WP

t_K

BO

Kostenkehre

Kostenkehre

Höchstpreis HP

Sättigungsmenge SM

Cournotscher Punkt CP

E(x)=K(x)

Gewinnschwelle x_u (Break-even-Point)

obere Gewinngrenze x_o

Gewinnbereich

Maximalgewinn

x_{opt}

Fixkosten

Fixkosten

Höchstpreis

Sättigungsmenge

Maximalgewinn

x_{Gmax}

maximale Stückzahlen x_{Gmax}

x_{opt}

Betriebsoptimum x_{opt}

Langfristige Preisuntergrenze LPU

LPU

Betriebsminimum x_{min}

x_{min}

Kurzfristige Preisuntergrenze KPU

KPU

t_{Kv}

x_{min}

t_{Kv}

T(x_{opt),LPU)

T(x_{min},KPU)

P(x)=k(x)

E'(x)

x_u

x_o

E'(x)

E_{max}

Maximalerlös

E_{max}

y3(x) = 0
Preisf(x) = (-2 * x) + 30
l1 = Solve(Preisf = 0)
Kostenf(x) = (0.1 * x^(3)) - (2 * x^(2)) + (15 * x) + 20
Fixkosten: Kostenf(0)
Dkvf(x) = (Kostenf(x) - Fixkosten) / x
k_{v}(x) = If[0 ≤ x ≤ Infinity, Dkvf(x)]
Dkvf' = Derivative(Dkvf(x), 1)
Xmin = Intersect(Dkvf', xAxis, (10, 0))
xbmin = If(Defined[Xmin], x(Xmin))
Erloesf = Simplify((Preisf(x) * x))
Gewinnf = Simplify(Erloesf(x) - Kostenf(x))
A, B, C = Intersect(Erloesf, Kostenf)
Kostenf' = Derivative(Kostenf, 1)
Kostenf'' = Derivative(Kostenf, 2)
Dkf(x) = Kostenf(x) / x
Sdkfk = Intersect(Dkf, Kostenf', (10.849529035917907, 6.91556794669612))
Dkf' = Derivative(Dkf, 1)
H = Intersect(Dkf', xAxis, (10.84952903592088, 0))
xopt = If(Defined[H], x(H))
LPU = If(Defined[Sdkfk], y(Sdkfk))
Gewinnf' = Derivative(Gewinnf, 1)
Gewinnf'' = Derivative(Gewinnf, 2)
I, J = Intersect(Gewinnf', xAxis)
xGmax = If(Gewinnf''(x(J)) < 0, x(J), x(I))
yGmax = If(Defined[xGmax], Gewinnf(xGmax))
Gmax = If(Defined[xGmax], Point[{(xGmax, yGmax)}])
D, GS, GG = Intersect(Gewinnf, xAxis)
CP = If(Defined[xGmax], Point[{(xGmax, Preisf(xGmax))}])
xmin: x(Xmin)
SM = Root(Preisf)
Saettigungsmenge = If(x(SM) ≥ 0, x(SM), Infinity)
Hoechstpreis: Preisf(0)
K(x) = If[0 ≤ x ≤ Infinity, Kostenf(x)]
Eingabefeld1 = Textfield(Kostenf)
a = true
P(x) = If[0 ≤ x ≤ Saettigungsmenge, Preisf(x)]
Eingabefeld2 = Textfield(Preisf)
b = true
HP = Point({(0, Hoechstpreis)})
E(x) = If[0 ≤ x ≤ Infinity, Erloesf(x)]
Text1: "E(x) =P(x)*x= " + Erloesf + ""
c = false
G(x) = If[0 ≤ x ≤ Infinity, Gewinnf(x)]
Text2: "G(x)=E(x)-K(x)= " + Gewinnf + ""
d = false
K'(x) = If[0 ≤ x ≤ Infinity, Kostenf'(x)]
e = false
G'(x) = If[0 ≤ x ≤ Infinity, Gewinnf'(x)]
g = false
G''(x) = If[0 ≤ x ≤ Infinity, Gewinnf''(x)]
f = false
K''(x) = If[0 ≤ x ≤ Infinity, Kostenf''(x)]
h = false
k(x) = If[0 ≤ x ≤ Infinity, Dkf(x)]
i = false
k'(x) = If[0 ≤ x ≤ Infinity, Dkf'(x)]
j = false
Text3: "k(x)=\frac{K(x)}{x}=" + (LaTeX[Dkf]) + ""
Text4: "k_v(x)=\frac{K_v(x)}{x}=" + (LaTeX[Dkvf]) + ""
l = false
k_{v}'(x) = If[0 ≤ x ≤ Infinity, Dkvf'(x)]
m = false
Text5: "x_{opt}=" + xopt + " ME"
Text6: "LPU= " + (LaTeX[LPU]) + " \frac{GE}{ME}"
Text7: "x_{min}=" + xmin + " ME"
KPU = If(Defined[xmin], k_{v}(xmin))
F = If(Defined[xmin], Point[{(xmin, KPU)}])
Text8: "KPU=" + (LaTeX[KPU]) + " \frac{GE}{ME}"
KK = Intersect(K'', xAxis)
yWP = If(x(KK) > 0, K(x(KK)))
Kostenkehre = If(x(KK) > 0, x(KK))
WP = If(x(KK) > 0, Point[{(Kostenkehre, yWP)}])
Text9: "Kostenkehre= " + Kostenkehre + " ME"
n = false
p = If(Defined[LPU], y = (LPU * x))
t_{K} = If(Defined[LPU], If[0 ≤ x ≤ Infinity, p(x)])
L = If(Defined[xopt], Point[{(xopt, K(xopt))}])
o = false
q = If(Defined[xopt], Segment[L, (xopt, 0)])
M = Point({(xopt, 0)})
Ursprung = Point({0})
r = Segment(Ursprung, KK)
s = Segment(WP, KK)
t = false
u = false
v = false
w = false
a_1 = false
b_1 = false
c_1 = false
Gewinnbereich = Segment(GS, GG)
d_1 = true
e_1 = false
f_1 = Segment(B, GS)
g_1 = Segment(C, GG)
h_1 = Segment(Ursprung, M)
FK = Point({(0, Fixkosten)})
i_1 = Segment(Ursprung, FK)
j_1 = false
k_1 = Segment(Ursprung, HP)
l_1 = Segment(Ursprung, SM)
N = Point({(x(Gmax), 0)})
p_1 = Segment(Gmax, N)
q_1 = Segment(Ursprung, N)
o_1 = false
r_1 = Segment(Ursprung, M)
s_1 = false
MM: M
t_1 = Segment(Sdkfk, MM)
u_1 = false
O = Point({(0, LPU)})
f_2 = Segment(Ursprung, O)
g_2 = Segment(O, Sdkfk)
v_1 = false
Q = Point({(x(F), 0)})
h_2 = Segment(Ursprung, Q)
i_2 = Segment(F, Q)
w_1 = false
R = Point({(0, KPU)})
j_2 = Segment(Ursprung, R)
k_2 = Segment(R, F)
NN: N
y4(x) = Fixkosten + (KPU * x)
p_2(x) = If[0 ≤ x ≤ Infinity, y4(x)]
S = Point({(xmin, K(xmin))})
QQ: Q
l_2 = Segment(Ursprung, QQ)
m_2 = Segment(S, QQ)
a_2 = false
b_2 = false
c_2 = false
d_2 = false
T = Intersect(k, P, (3.4491251520748367, 23.18290312830983))
U = Intersect(P, k, (3.4231605918590313, 15.184523943769586))
W, Z = Intersect(Dkf, Preisf, 0.001, Saettigungsmenge)
n_2 = Segment(W, (x(W), 0))
q_2 = Segment(Z, (x(Z), 0))
xu: x(GS)
xo: x(GG)
e_2(x) = xu ≤ x ≤ xo
o_2 = false
A_1 = Point({xu, 0})
B_1 = Point({(xo, 0)})
Erloesf' = Derivative(Erloesf, 1)
r_2(x) = If[0 ≤ x ≤ Saettigungsmenge, Erloesf'(x)]
C_1 = Root(Erloesf', 0, Saettigungsmenge)
D_1 = Point({(x(C_1), Erloesf(x(C_1)))})
s_2 = Segment(D_1, C_1)
t_2 = false
V = Intersect(k, P, (1.3497258428648307, 27.3005483083821))