# Реферат: Риск в задачах линейного программирования

Лабораторная работа №3<span Times New Roman",«serif»; mso-ansi-language:EN-US">

Риск в задачах линейногопрограммирования.

Задание:

Предприятие выпускает 2 видапродукции в объмах Н1 и Н2.

Известен случайный векторограничений -<span Times New Roman",«serif»">

<img src="/cache/referats/12872/image002.gif" v:shapes="_x0000_i1025">

и вектор цен на продукцию –

<img src="/cache/referats/12872/image004.gif" v:shapes="_x0000_i1026">

<div v:shape="_x0000_s1036">

0,7

<div v:shape="_x0000_s1031">

0,8

<div v:shape="_x0000_s1035">

0,5

<div v:shape="_x0000_s1032">

0,6

<div v:shape="_x0000_s1033">

0,4

<div v:shape="_x0000_s1034">

0,5

<div v:shape="_x0000_s1030">

0,2

<span Times New Roman",«serif»;mso-ansi-language:EN-US">:<span Times New Roman",«serif»">

<img src="/cache/referats/12872/image005.gif" v:shapes="_x0000_s1039"> <img src="/cache/referats/12872/image006.gif" v:shapes="_x0000_s1046"> <img src="/cache/referats/12872/image007.gif" v:shapes="_x0000_s1040"> <img src="/cache/referats/12872/image008.gif" v:shapes="_x0000_s1045"> <img src="/cache/referats/12872/image009.gif" v:shapes="_x0000_s1041"> <img src="/cache/referats/12872/image010.gif" v:shapes="_x0000_s1044"> <img src="/cache/referats/12872/image011.gif" v:shapes="_x0000_s1042"> <img src="/cache/referats/12872/image006.gif" v:shapes="_x0000_s1043">

<span Courier New";mso-bidi-font-family:«Times New Roman»">

<span Courier New";mso-bidi-font-family:«Times New Roman»">

<span Courier New";mso-bidi-font-family: «Times New Roman»">а11 = 1,1 + 0,01 *

<span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">N <span Courier New"; mso-bidi-font-family:«Times New Roman»">или <span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">1,5 + <span Courier New"; mso-bidi-font-family:«Times New Roman»">0,01 * <span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">N

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">a12= 3

<span Courier New";mso-bidi-font-family:«Times New Roman»">,<span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">1 + <span Courier New"; mso-bidi-font-family:«Times New Roman»">0,01 * <span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">N или 3,3 + <span Courier New"; mso-bidi-font-family:«Times New Roman»">0,01 * <span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">N

<span Courier New";mso-bidi-font-family: «Times New Roman»">

<span Courier New";mso-bidi-font-family:«Times New Roman»">

<div v:shape="_x0000_s1037">

0,3

<span Courier New";mso-bidi-font-family: «Times New Roman»">а21 = 2,2 + 0,01 * <span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">N <span Courier New"; mso-bidi-font-family:«Times New Roman»">или <span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">2,7 + <span Courier New"; mso-bidi-font-family:«Times New Roman»">0,01 * <span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">N

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">a22= 4

<span Courier New";mso-bidi-font-family:«Times New Roman»">,<span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">1 + <span Courier New"; mso-bidi-font-family:«Times New Roman»">0,01 * <span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">N или 4,5 + <span Courier New"; mso-bidi-font-family:«Times New Roman»">0,01 * <span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">N

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">a11= 1,31

<span Courier New";mso-bidi-font-family:«Times New Roman»">свероятностью <span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">p = 0,2

<span Courier New";mso-bidi-font-family: «Times New Roman»">или

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US"> a11 = 1,71<span Courier New";mso-bidi-font-family:«Times New Roman»">свероятностью <span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">p = 0,2

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">a12= 3,31

<span Courier New";mso-bidi-font-family:«Times New Roman»">свероятностью <span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">p = 0,8

<span Courier New";mso-bidi-font-family: «Times New Roman»">или

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US"> a12 = 3,51<span Courier New";mso-bidi-font-family:«Times New Roman»">свероятностью <span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">p = 0,2

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">a21= 2,41

<span Courier New";mso-bidi-font-family:«Times New Roman»">свероятностью <span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">p = 0,4

<span Courier New";mso-bidi-font-family: «Times New Roman»">или

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US"> a21 = 2,91<span Courier New";mso-bidi-font-family:«Times New Roman»">свероятностью <span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">p = 0,2

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">a22= 4,31

<span Courier New";mso-bidi-font-family:«Times New Roman»">свероятностью <span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">p = 0,6

<span Courier New";mso-bidi-font-family: «Times New Roman»">или

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US"> a22 = 4,71<span Courier New";mso-bidi-font-family:«Times New Roman»">свероятностью <span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">p = 0,2

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">

<span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">Решени

<span Courier New"; mso-bidi-font-family:«Times New Roman»">е<span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">:

<span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">

<img src="/cache/referats/12872/image013.gif" v:shapes="_x0000_i1027"><span Times New Roman",«serif»; mso-ansi-language:EN-US">;

<span Times New Roman",«serif»">

<img src="/cache/referats/12872/image015.gif" v:shapes="_x0000_i1028">

<img src="/cache/referats/12872/image017.gif" v:shapes="_x0000_i1029">

<span Times New Roman";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:RU;mso-fareast-language:RU;mso-bidi-language:AR-SA">

Различаютальтернативные варианты матрицы<span Times New Roman",«serif»;mso-ansi-language:EN-US">:

<span Times New Roman",«serif»;mso-ansi-language:EN-US">

<span Times New Roman",«serif»; mso-ansi-language:EN-US">1) <img src="/cache/referats/12872/image019.gif" v:shapes="_x0000_i1030">          2) <img src="/cache/referats/12872/image021.gif" v:shapes="_x0000_i1031">          3) <img src="/cache/referats/12872/image023.gif" v:shapes="_x0000_i1032">          4) <img src="/cache/referats/12872/image025.gif" v:shapes="_x0000_i1033">

<span Times New Roman",«serif»; mso-ansi-language:EN-US">5) <img src="/cache/referats/12872/image027.gif" v:shapes="_x0000_i1034">          6) <img src="/cache/referats/12872/image029.gif" v:shapes="_x0000_i1035">          7) <img src="/cache/referats/12872/image031.gif" v:shapes="_x0000_i1036">          8) <img src="/cache/referats/12872/image033.gif" v:shapes="_x0000_i1037">

<span Times New Roman",«serif»; mso-ansi-language:EN-US">9) <img src="/cache/referats/12872/image035.gif" v:shapes="_x0000_i1038">          10) <img src="/cache/referats/12872/image037.gif" v:shapes="_x0000_i1039">        11) <img src="/cache/referats/12872/image039.gif" v:shapes="_x0000_i1040">        12) <img src="/cache/referats/12872/image041.gif" v:shapes="_x0000_i1041">

<span Times New Roman",«serif»; mso-ansi-language:EN-US">13) <img src="/cache/referats/12872/image043.gif" v:shapes="_x0000_i1042">        14) <img src="/cache/referats/12872/image045.gif" v:shapes="_x0000_i1043">        15) <img src="/cache/referats/12872/image047.gif" v:shapes="_x0000_i1044">        16) <img src="/cache/referats/12872/image049.gif" v:shapes="_x0000_i1045">

<span Courier New";mso-bidi-font-family: «Times New Roman»">

<span Courier New";mso-bidi-font-family: «Times New Roman»">Составим задачи линейного программирования, соответствующиекаждому значению матрицы А, которые достигаются с известными вероятностями.Каждую из этих задач решим на ЭВМ симплекс-методом.

<span Courier New"; mso-bidi-font-family:«Times New Roman»">

<span Courier New"; mso-bidi-font-family:«Times New Roman»"><img src="/cache/referats/12872/image051.gif" v:shapes="_x0000_i1046">

<span Courier New"; mso-bidi-font-family:«Times New Roman»"><img src="/cache/referats/12872/image053.gif" v:shapes="_x0000_i1047">

<span Courier New"; mso-bidi-font-family:«Times New Roman»">

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">

<span Courier New"; mso-bidi-font-family:«Times New Roman»">1) <span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">x1 = 0;         x2= 42,24924;z = 126,3252;p = 0,012

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US"> 2

<span Courier New"; mso-bidi-font-family:«Times New Roman»">) <span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">x1 = 0;         x2= 42,24924;z = 126,3252;p = 0,048

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">

<span Courier New"; mso-bidi-font-family:«Times New Roman»">3) <span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">x1 = 0;         x2= 39,82808;z = 119,086;  p = 0,018

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">

<span Courier New"; mso-bidi-font-family:«Times New Roman»">4) <span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">x1 = 107,7519;  x2 = 0;        z = 149,7752;p = 0,012

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US"> 5

<span Courier New"; mso-bidi-font-family:«Times New Roman»">) <span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">x1 = 107,7519;  x2 = 0;        z = 149,7752;p = 0,028

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">

<span Courier New"; mso-bidi-font-family:«Times New Roman»">6) <span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">x1 = 0;         x2= 39,82808;z = 119,086;  p = 0,072

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">

<span Courier New"; mso-bidi-font-family:«Times New Roman»">7) <span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">x1 = 107,7519;  x2 = 0;        z = 149,7752;p = 0,056

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">

<span Courier New"; mso-bidi-font-family:«Times New Roman»">8) <span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">x1 = 0;         x2= 42,24924;z = 126,3252;p = 0,048

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">

<span Courier New"; mso-bidi-font-family:«Times New Roman»">9) <span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">x1 = 107,7519;  x2 = 0;        z = 149,7752;p = 0,028

<span Courier New";mso-bidi-font-family: «Times New Roman»">10)

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">x1 =0;         x2 = 39,82808;z = 119,086;  p= 0,168

<span Courier New";mso-bidi-font-family: «Times New Roman»">11)

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">x1 =107,7519;  x2 = 0;        z =149,7752;p = 0,018

<span Courier New";mso-bidi-font-family: «Times New Roman»">12)

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">x1 =0;         x2 = 39,82808;z = 119,086;  p= 0,072

<span Courier New";mso-bidi-font-family: «Times New Roman»">13)

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">x1 =107,7519;  x2 = 0;        z =149,7752;p = 0,042

<span Courier New";mso-bidi-font-family: «Times New Roman»">14)

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">x1 =0;         x2 = 42,24924;z = 126,3252;p= 0,112

<span Courier New";mso-bidi-font-family: «Times New Roman»">15)

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">x1 =0;         x2 = 39,82808;z = 119,086;  p= 0,168

<span Courier New";mso-bidi-font-family: «Times New Roman»">1

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">6<span Courier New";mso-bidi-font-family:«Times New Roman»">) <span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">x1 = 0;         x2= 39,82808;z = 119,086;  p = 0,168

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">

<span Courier New";mso-bidi-font-family:«Times New Roman»">Распределениеслучайной величины у максимального дохода полученное в результате вычислений

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">:

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">

Z

<span Courier New";mso-bidi-font-family:«Times New Roman»">126,32

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">126,32

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">119,086

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">149,77

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">149,77

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">119,086

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">149,77

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">126,32

<span Courier New";mso-bidi-font-family: «Times New Roman»;color:white;mso-ansi-language:EN-US">P

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">0,012

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">0,048

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">0,018

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">0,012

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">0,028

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">0,072

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">0,056

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">0,048

Z<span Courier New";mso-bidi-font-family:«Times New Roman»;color:white;mso-ansi-language: EN-US">

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">149,77

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">119,086

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">149,77

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">119,08

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">149,77

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">126,32

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">119,08

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">119,08

<span Courier New";mso-bidi-font-family: «Times New Roman»;color:white;mso-ansi-language:EN-US">P

<span Courier New";mso-bidi-font-family:«Times New Roman»;color:white;mso-ansi-language: EN-US">

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">0,028

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">0,168

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">0,018

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">0,168

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">0,042

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">0,112

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">0,168

<span Courier New";mso-bidi-font-family: «Times New Roman»;mso-ansi-language:EN-US">0,168

<span Courier New"; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US">

1)<span Times New Roman"">

<span Times New Roman",«serif»;mso-ansi-language:EN-US">                 M(z) = 149,7*0,012 + 126

<span Times New Roman",«serif»">,3*0,048 + 119,08*0,018 + 149,7*0,012+ 149,7*0,028 +

<span Times New Roman",«serif»">+119,08*0,072 + 149,7*0,056 + 126,3*0,048 + 149,7*0,028 + 119,08*0,168 + 149,7*0,018+ 119,08*0,072 + 149,7*0,028 + 119,08*0,168 + 149,7*0,018 + 119,08*0,072 + 126,3*0,012+ 119,08*0,168 + 119,08*0,168 = 115,985

<span Courier New"; mso-bidi-font-family:«Times New Roman»">

<span Courier New";mso-fareast-font-family:«Courier New»">2)<span Times New Roman"">

<span Courier New";mso-bidi-font-family:«Times New Roman»">Определимвеличину максимального дохода, а также соответствующую технологию выпускапродукции.

<span Courier New";mso-bidi-font-family:«Times New Roman»">

<span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">Zmax = Z12 = 119,08

<span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">P12 = P15 = 0,168 = max

<span Courier New";mso-bidi-font-family:«Times New Roman»">знач.<span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">

<span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">

<span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">Aopt1 = A12 = <img src="/cache/referats/12872/image055.gif" v:shapes="_x0000_i1048">

<span Courier New";mso-bidi-font-family:«Times New Roman»">или

<span Times New Roman",«serif»">

<span Courier New";mso-bidi-font-family:«Times New Roman»; mso-ansi-language:EN-US">Aopt2 = A15 = <img src="/cache/referats/12872/image057.gif" v:shapes="_x0000_i1049">

<span Times New Roman",«serif»">
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