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»">