Ergebnisse (Kosten- und Preistheorie)

1. 1. K(x) = 1,2x + 300
   2. K(x) = 2,5x + 500
   3. K(x) = 2x + 800
2. K(x) = 1,5x + 250 / 500 / nein
3. 1. K¯(x) = 0,1x + 2 + 40/x; x_opt = 20; K¯(x_opt) = 6
   2. K¯(x) = 0,05x + 1,6 + 28,8/x; x_opt = 24; K¯(x_opt) = 4
   3. K¯(x) = 0,03x + 0,5 + 50/x; x_opt ~ 41; K¯(x_opt) = 2,95
   4. K¯(x) = 0,01x + 0,25 + 72/x; x_opt ~85; K¯(x_opt) = 1,95
4. 1. K(x) = 0,001x² + 5x + 250; x_opt = 500; K¯(x_opt) = 6
   2. K(x) = 0,0025x² + 6x + 800; x_opt = ~566; K¯(x_opt) = 8,83
   3. K(x) = 0,1x² + 5x + 800; x_opt ~ 89; K¯(x_opt) = 22,89
   4. K(x) = 0,1x² + 20x + 1000; x_opt = 100; K¯(x_opt) = 40
   5. K(x) = 0,005x² + 1120; x_opt ~ 473; K¯(x_opt) = 4,73
5. 1. K(x) = 0,02x² + 80x + 800; x_opt = 200; K¯(x_opt) = 88
   2. K(x) = 0,005x² + 12x + 1800; x_opt = 600; K¯(x_opt) = 18
6. 1. x_W = 2; x_opt ~ 8; x_min = 3; LPU = 9,55; KPU = 4,55
   2. x_W = 50; x_opt ~ 79; x_min = 75; LPU = 80,48; KPU = 67,5
   3. x_W = 250; x_opt ~ 408; x_min = 375; LPU = 87,42; KPU = 59,38
   4. x_W = 25; x_opt ~57; x_min = 37,5; LPU = 8,83; KPU = 3,69
7. x_W = 10; x_min = 15
8. 1. K(x) = 0,02x³ - 3x² + 180 x + 1000
   2. K(x) = 0,01x³ - 0,4x² + 6x + 200
   3. K(x) = 0,025x³ - 0,75x² + 60x + 3200
   4. K(x) = 0,002x³ - 0,18x² + 7,8x + 9450
9. K(x) = 0,001x³ - 0,2x² + 180x + 36000; x_W ~ 67
10. 1. x₁ = 10; x₂ = 40; x_Gmax = 25; Gmax = 22,5
    2. x₁ = 20; x₂ = 260; x_Gmax = 140; Gmax = 720
    3. x₁ = 400; x₂ = 1600; x_Gmax = 1000; Gmax = 720
    4. x₁ = 900; x₂ = 10000; x_Gmax = 5450; Gmax = 20702,50
    5. x₁ = 70; x₂ = 270; x_Gmax ~ 181; Gmax = 8515,70
    6. x₁ ~ 227; x₂ ~ 604; x_Gmax ~ 448; Gmax = 18252,60
11. 1. p(x) = -0,2x + 60; p_max = 60; x_S = 300; x_Emax = 150
    2. p(x) = -0,1x + 180; p_max = 180; x_S = 1800; x_Emax = 900
    3. p(x) = -0,25x + 150; p_max = 150; x_S = 600; x_Emax = 300
    4. p(x) = -0,05x + 25; p_max = 25; x_S = 500; x_Emax = 250
12. 1. p(x) = 0,01x² - 2,6x + 160; p_max = 160; x_S = 100; x_Emax = 40
    2. p(x) = 0,001x² - 1,6x + 550; p_max = 550; x_S = 500; x_Emax ~ 215
    3. p(x) = -0,015x² + 24; p_max = 24; x_S = 40; x_Emax ~ 23
13. 1. x₁ = 10; x₂ = 50; C(30/13)
    2. x₁ ~ 14; x₂ ~ 536; C(275/54)
    3. x₁ ~ 17; x₂ ~ 133; C(75/4)
    4. x₁ = 80; x₂ = 4220; C(2150/78,50)
14. 1. x_Gmax = 30; p_Gmax = 12; Gmax = 70
    2. x_Gmax ~ 67; p_Gmax = 16,65; Gmax = 501,87
    3. x_Gmax = 10; p_Gmax = 60; Gmax = 230
    4. x_Gmax ~ 25; p_Gmax = 30; Gmax = 282,50
15. x₁ ~ 7; x₂ ~ 57; C(32/45); Gmax = 780
16. K(x) = 0,01x² + 7x + 400; x₁ = 20; x₂ = 400; C(210/19,6)
17. K(x) = 0,025x² + 60x + 8000; C(1500/202,50); Gmax = 149500
18. K(x) = 0,1x³ - 2x² + 25x + 1450; x₂ ~ 26; C(18/128); Gmax = 468,80
19. p(x) = -0,05x + 80; x₁ = 60; x₂ = 300; C(180/71)
20. 1. 6
    2. 4
    3. 12

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