а) Производственная задача, максимизация прибыли. Имеются

```&Igrave;&icirc;&ntilde;&ecirc;&icirc;&acirc;&ntilde;&ecirc;&egrave;&eacute; &ocirc;&egrave;&ccedil;&egrave;&ecirc;&icirc;-&ograve;&aring;&otilde;&iacute;&egrave;&divide;&aring;&ntilde;&ecirc;&egrave;&eacute; &egrave;&iacute;&ntilde;&ograve;&egrave;&ograve;&oacute;&ograve; (&Atilde;&Oacute;)
&Ocirc;&agrave;&ecirc;&oacute;&euml;&uuml;&ograve;&aring;&ograve; &egrave;&iacute;&iacute;&icirc;&acirc;&agrave;&ouml;&egrave;&eacute; &egrave; &acirc;&ucirc;&ntilde;&icirc;&ecirc;&egrave;&otilde; &ograve;&aring;&otilde;&iacute;&icirc;&euml;&icirc;&atilde;&egrave;&eacute;
&Igrave;&aring;&ograve;&icirc;&auml;&ucirc; &icirc;&iuml;&ograve;&egrave;&igrave;&egrave;&ccedil;&agrave;&ouml;&egrave;&egrave;, &acirc;&aring;&ntilde;&iacute;&agrave; 2014
&Ntilde;&aring;&igrave;&egrave;&iacute;&agrave;&eth; 7, &ccedil;&agrave;&auml;&agrave;&divide;&egrave; &euml;&egrave;&iacute;&aring;&eacute;&iacute;&icirc;&atilde;&icirc; &iuml;&eth;&icirc;&atilde;&eth;&agrave;&igrave;&igrave;&egrave;&eth;&icirc;&acirc;&agrave;&iacute;&egrave;&yuml;
&Icirc;&aacute;&ugrave;&aring;&eacute; &ccedil;&agrave;&auml;&agrave;&divide;&aring;&eacute;
&euml;&egrave;&iacute;&aring;&eacute;&iacute;&icirc;&atilde;&icirc; &iuml;&eth;&icirc;&atilde;&eth;&agrave;&igrave;&igrave;&egrave;&eth;&icirc;&acirc;&agrave;&iacute;&egrave;&yuml; &iacute;&agrave;&ccedil;&ucirc;&acirc;&agrave;&aring;&ograve;&ntilde;&yuml; &ccedil;&agrave;&auml;&agrave;&divide;&agrave; &acirc;&egrave;&auml;&agrave;
hc, xi → inf,
xj &gt; 0, j ∈ I+ ,
hai , bi 6 bi , i = 1, . . . , m,
hai , bi = bi , i = m + 1, . . . , s,
&atilde;&auml;&aring; I+ ⊂ {1, . . . , n}.
1. &Iuml;&aring;&eth;&aring;&iuml;&egrave;&oslash;&egrave;&ograve;&aring; &icirc;&aacute;&ugrave;&oacute;&thorn; &ccedil;&agrave;&auml;&agrave;&divide;&oacute; &acirc; &igrave;&agrave;&ograve;&eth;&egrave;&divide;&iacute;&icirc;&eacute; &ocirc;&icirc;&eth;&igrave;&aring;, &ntilde;&divide;&egrave;&ograve;&agrave;&yuml; &divide;&ograve;&icirc; I+ = {1, . . . , k}.
&Ecirc;&agrave;&iacute;&icirc;&iacute;&egrave;&divide;&aring;&ntilde;&ecirc;&icirc;&eacute; &ccedil;&agrave;&auml;&agrave;&divide;&aring;&eacute; &euml;&egrave;&iacute;&aring;&eacute;&iacute;&icirc;&atilde;&icirc; &iuml;&eth;&icirc;&atilde;&eth;&agrave;&igrave;&igrave;&egrave;&eth;&icirc;&acirc;&agrave;&iacute;&egrave;&yuml; &iacute;&agrave;&ccedil;&ucirc;&acirc;&agrave;&aring;&ograve;&ntilde;&yuml; &ccedil;&agrave;&auml;&agrave;&divide;&agrave; &acirc;&egrave;&auml;&agrave;
hc, xi → inf,
x &gt; 0,
Ax = b.
&Icirc;&ntilde;&iacute;&icirc;&acirc;&iacute;&icirc;&eacute; (&ntilde;&ograve;&agrave;&iacute;&auml;&agrave;&eth;&ograve;&iacute;&icirc;&eacute;) &ccedil;&agrave;&auml;&agrave;&divide;&aring;&eacute;
&acirc;&egrave;&auml;&agrave;
&euml;&egrave;&iacute;&aring;&eacute;&iacute;&icirc;&atilde;&icirc; &iuml;&eth;&icirc;&atilde;&eth;&agrave;&igrave;&igrave;&egrave;&eth;&icirc;&acirc;&agrave;&iacute;&egrave;&yuml; &iacute;&agrave;&ccedil;&ucirc;&acirc;&agrave;&aring;&ograve;&ntilde;&yuml; &ccedil;&agrave;&auml;&agrave;&divide;&agrave;
hc, xi → inf,
x &gt; 0,
Ãx 6 b̃.
2. &Iuml;&icirc;&ecirc;&agrave;&aelig;&egrave;&ograve;&aring;, &divide;&ograve;&icirc; &ecirc;&agrave;&iacute;&icirc;&iacute;&egrave;&divide;&aring;&ntilde;&ecirc;&agrave;&yuml; &egrave; &icirc;&ntilde;&iacute;&icirc;&acirc;&iacute;&agrave;&yuml; &ccedil;&agrave;&auml;&agrave;&divide;&agrave; &ntilde;&acirc;&icirc;&auml;&yuml;&ograve;&ntilde;&yuml; &auml;&eth;&oacute;&atilde; &ecirc; &auml;&eth;&oacute;&atilde;&oacute;, &agrave; &icirc;&aacute;&ugrave;&agrave;&yuml; &ecirc; &euml;&thorn;&aacute;&icirc;&eacute; &egrave;&ccedil; &iacute;&egrave;&otilde;.
3. &Ocirc;&icirc;&eth;&igrave;&agrave;&euml;&egrave;&ccedil;&oacute;&eacute;&ograve;&aring; &acirc; &acirc;&egrave;&auml;&aring; &ccedil;&agrave;&auml;&agrave;&divide; &euml;&egrave;&iacute;&aring;&eacute;&iacute;&icirc;&atilde;&icirc; &iuml;&eth;&icirc;&atilde;&eth;&agrave;&igrave;&igrave;&egrave;&eth;&icirc;&acirc;&agrave;&iacute;&egrave;&yuml; &ntilde;&euml;&aring;&auml;&oacute;&thorn;&ugrave;&egrave;&aring; &ograve;&aring;&otilde;&iacute;&egrave;&ecirc;&icirc;&yacute;&ecirc;&icirc;&iacute;&icirc;&igrave;&egrave;&divide;&aring;&ntilde;&ecirc;&egrave;&aring; &ccedil;&agrave;&auml;&agrave;&divide;&egrave;:
a) &Iuml;&eth;&icirc;&egrave;&ccedil;&acirc;&icirc;&auml;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&agrave;&yuml; &ccedil;&agrave;&auml;&agrave;&divide;&agrave;, &igrave;&agrave;&ecirc;&ntilde;&egrave;&igrave;&egrave;&ccedil;&agrave;&ouml;&egrave;&yuml; &iuml;&eth;&egrave;&aacute;&ucirc;&euml;&egrave;. &Egrave;&igrave;&aring;&thorn;&ograve;&ntilde;&yuml; n &ograve;&icirc;&acirc;&agrave;&eth;&icirc;&acirc; &egrave; m &eth;&aring;&ntilde;&oacute;&eth;&ntilde;&icirc;&acirc;. &Iacute;&agrave;&divide;&agrave;&euml;&uuml;&iacute;&ucirc;&aring; &ccedil;&agrave;&iuml;&agrave;&ntilde;&ucirc; j -&atilde;&icirc; &eth;&aring;&ntilde;&oacute;&eth;&ntilde;&agrave; &eth;&agrave;&acirc;&iacute;&ucirc; xj . &Ouml;&aring;&iacute;&agrave; i-&atilde;&icirc; &ograve;&icirc;&acirc;&agrave;&eth;&agrave; &eth;&agrave;&acirc;&iacute;&agrave; pi . &Auml;&euml;&yuml;
&iuml;&eth;&icirc;&egrave;&ccedil;&acirc;&icirc;&auml;&ntilde;&ograve;&acirc;&agrave; &aring;&auml;&egrave;&iacute;&egrave;&ouml;&ucirc; i-&atilde;&icirc; &ograve;&icirc;&acirc;&agrave;&eth;&agrave; &iacute;&oacute;&aelig;&iacute;&icirc; aij &aring;&auml;&egrave;&iacute;&egrave;&ouml; j -&atilde;&icirc; &eth;&aring;&ntilde;&oacute;&eth;&ntilde;&agrave;. &Ograve;&eth;&aring;&aacute;&oacute;&aring;&ograve;&ntilde;&yuml; &igrave;&agrave;&ecirc;&ntilde;&egrave;&igrave;&egrave;&ccedil;&egrave;&eth;&icirc;&acirc;&agrave;&ograve;&uuml; &ntilde;&oacute;&igrave;&igrave;&agrave;&eth;&iacute;&oacute;&thorn; &ntilde;&ograve;&icirc;&egrave;&igrave;&icirc;&ntilde;&ograve;&uuml; &iuml;&eth;&icirc;&egrave;&ccedil;&acirc;&aring;&auml;&frac14;&iacute;&iacute;&icirc;&atilde;&icirc; &ograve;&icirc;&acirc;&agrave;&eth;&agrave;.
b) &Iuml;&eth;&icirc;&egrave;&ccedil;&acirc;&icirc;&auml;&ntilde;&ograve;&acirc;&aring;&iacute;&iacute;&agrave;&yuml; &ccedil;&agrave;&auml;&agrave;&divide;&agrave;, &igrave;&egrave;&iacute;&egrave;&igrave;&egrave;&ccedil;&agrave;&ouml;&egrave;&yuml; &egrave;&ccedil;&auml;&aring;&eth;&aelig;&aring;&ecirc;. &Egrave;&igrave;&aring;&thorn;&ograve;&ntilde;&yuml; n &ograve;&icirc;&acirc;&agrave;&eth;&icirc;&acirc; &egrave; m &eth;&aring;&ntilde;&oacute;&eth;&ntilde;&icirc;&acirc;. &Ouml;&aring;&iacute;&agrave; j -&atilde;&icirc; &eth;&aring;&ntilde;&oacute;&eth;&ntilde;&agrave; &eth;&agrave;&acirc;&iacute;&agrave; qj . &Auml;&euml;&yuml; &iuml;&eth;&icirc;&egrave;&ccedil;&acirc;&icirc;&auml;&ntilde;&ograve;&acirc;&agrave; &aring;&auml;&egrave;&iacute;&egrave;&ouml;&ucirc; i-&atilde;&icirc; &ograve;&icirc;&acirc;&agrave;&eth;&agrave; &iacute;&oacute;&aelig;&iacute;&icirc;
aij &aring;&auml;&egrave;&iacute;&egrave;&ouml; j -&atilde;&icirc; &eth;&aring;&ntilde;&oacute;&eth;&ntilde;&agrave;. &Ograve;&eth;&aring;&aacute;&oacute;&aring;&ograve;&ntilde;&yuml; &igrave;&egrave;&iacute;&egrave;&igrave;&egrave;&ccedil;&egrave;&eth;&icirc;&acirc;&agrave;&ograve;&uuml; &icirc;&aacute;&ugrave;&oacute;&thorn; &ntilde;&ograve;&icirc;&egrave;&igrave;&icirc;&ntilde;&ograve;&uuml; &iuml;&eth;&icirc;&egrave;&ccedil;&acirc;&icirc;&auml;&ntilde;&ograve;&acirc;&agrave; yi &aring;&auml;&egrave;&iacute;&egrave;&ouml; i-&atilde;&icirc; &ograve;&icirc;&acirc;&agrave;&eth;&agrave;.
c) &Ograve;&eth;&agrave;&iacute;&ntilde;&iuml;&icirc;&eth;&ograve;&iacute;&agrave;&yuml; &ccedil;&agrave;&auml;&agrave;&divide;&agrave;. &Egrave;&igrave;&aring;&aring;&ograve;&ntilde;&yuml; n &iuml;&eth;&icirc;&egrave;&ccedil;&acirc;&icirc;&auml;&egrave;&ograve;&aring;&euml;&aring;&eacute; &egrave; m &iuml;&icirc;&ograve;&eth;&aring;&aacute;&egrave;&ograve;&aring;&euml;&aring;&eacute; &iacute;&aring;&ecirc;&icirc;&ograve;&icirc;&eth;&icirc;&eacute;
&iuml;&eth;&icirc;&auml;&oacute;&ecirc;&ouml;&egrave;&egrave;. &Iuml;&eth;&icirc;&egrave;&ccedil;&acirc;&icirc;&auml;&egrave;&ograve;&aring;&euml;&uuml; i &igrave;&icirc;&aelig;&aring;&ograve; &iuml;&eth;&icirc;&egrave;&ccedil;&acirc;&aring;&ntilde;&ograve;&egrave; &iacute;&aring; &aacute;&icirc;&euml;&aring;&aring; xi &aring;&auml;&egrave;&iacute;&egrave;&ouml;, &iuml;&icirc;&ograve;&eth;&aring;&aacute;&egrave;&ograve;&aring;&euml;&thorn;
j &ograve;&eth;&aring;&aacute;&oacute;&aring;&ograve;&ntilde;&yuml; &iacute;&aring; &igrave;&aring;&iacute;&uuml;&oslash;&aring; yj &aring;&auml;&egrave;&iacute;&egrave;&ouml;. &Auml;&icirc;&ntilde;&ograve;&agrave;&acirc;&ecirc;&agrave; &icirc;&auml;&iacute;&icirc;&eacute; &aring;&auml;&egrave;&iacute;&egrave;&ouml;&ucirc; &icirc;&ograve; &iuml;&eth;&icirc;&egrave;&ccedil;&acirc;&icirc;&auml;&egrave;&ograve;&aring;&euml;&yuml; i
&ecirc; &iuml;&icirc;&ograve;&eth;&aring;&aacute;&egrave;&ograve;&aring;&euml;&thorn; j &ntilde;&ograve;&icirc;&egrave;&ograve; aij . &Ograve;&eth;&aring;&aacute;&oacute;&aring;&ograve;&ntilde;&yuml; &icirc;&aacute;&aring;&ntilde;&iuml;&aring;&divide;&egrave;&ograve;&uuml; &acirc;&ntilde;&aring; &iuml;&icirc;&ograve;&eth;&aring;&aacute;&iacute;&icirc;&ntilde;&ograve;&egrave;, &ccedil;&agrave;&ograve;&eth;&agrave;&ograve;&egrave;&acirc; &iacute;&agrave;&egrave;&igrave;&aring;&iacute;&uuml;&oslash;&oacute;&thorn; &ntilde;&oacute;&igrave;&igrave;&oacute;.
d) &Ograve;&eth;&agrave;&iacute;&ntilde;&iuml;&icirc;&eth;&ograve;&iacute;&agrave;&yuml; &ccedil;&agrave;&auml;&agrave;&divide;&agrave; &acirc; &ntilde;&aring;&ograve;&egrave;. &Agrave;&iacute;&agrave;&euml;&icirc;&atilde;&egrave;&divide;&iacute;&icirc; &iuml;&eth;&aring;&auml;&ucirc;&auml;&oacute;&ugrave;&aring;&igrave;&oacute;, &iacute;&icirc; &iuml;&eth;&icirc;&egrave;&ccedil;&acirc;&icirc;&auml;&egrave;&ograve;&aring;&euml;&egrave; &egrave; &iuml;&icirc;&ograve;&eth;&aring;&aacute;&egrave;&ograve;&aring;&euml;&egrave; &ntilde;&icirc;&aring;&auml;&egrave;&iacute;&aring;&iacute;&ucirc; &acirc; &ntilde;&aring;&ograve;&uuml; (&icirc;&eth;&egrave;&aring;&iacute;&ograve;&egrave;&eth;&icirc;&acirc;&agrave;&iacute;&iacute;&ucirc;&eacute; &atilde;&eth;&agrave;&ocirc; &aacute;&aring;&ccedil; &ouml;&egrave;&ecirc;&euml;&icirc;&acirc;), &iacute;&agrave; &ecirc;&agrave;&aelig;&auml;&icirc;&igrave; &eth;&aring;&aacute;&eth;&aring;
&ecirc;&icirc;&ograve;&icirc;&eth;&icirc;&eacute; &ccedil;&agrave;&auml;&agrave;&iacute;&agrave; &iuml;&eth;&icirc;&iuml;&oacute;&ntilde;&ecirc;&iacute;&agrave;&yuml; &ntilde;&iuml;&icirc;&ntilde;&icirc;&aacute;&iacute;&icirc;&ntilde;&ograve;&uuml;, &ecirc;&icirc;&ograve;&icirc;&eth;&oacute;&thorn; &iacute;&aring;&euml;&uuml;&ccedil;&yuml; &iuml;&eth;&aring;&acirc;&ucirc;&oslash;&agrave;&ograve;&uuml;.
&Euml;&egrave;&iacute;&aring;&eacute;&iacute;&ucirc;&aring; &eth;&agrave;&acirc;&aring;&iacute;&ntilde;&ograve;&acirc;&agrave; &egrave; &iacute;&aring;&eth;&agrave;&acirc;&aring;&iacute;&ntilde;&ograve;&acirc;&agrave; &ccedil;&agrave;&auml;&agrave;&thorn;&ograve; &iacute;&aring;&ecirc;&icirc;&ograve;&icirc;&eth;&icirc;&aring; &igrave;&iacute;&icirc;&atilde;&icirc;&atilde;&eth;&agrave;&iacute;&iacute;&icirc;&aring; &igrave;&iacute;&icirc;&aelig;&aring;&ntilde;&ograve;&acirc;&icirc; (&iuml;&icirc;&euml;&egrave;&yacute;&auml;&eth;) X . &Ograve;&icirc;&divide;&ecirc;&agrave; v &iacute;&agrave;&ccedil;&ucirc;&acirc;&agrave;&aring;&ograve;&ntilde;&yuml; &oacute;&atilde;&euml;&icirc;&acirc;&icirc;&eacute; &ograve;&icirc;&divide;&ecirc;&icirc;&eacute; X , &aring;&ntilde;&euml;&egrave; &egrave;&ccedil; v = αu + (1 − α)w, u ∈ X ,
w ∈ X , α ∈ (0, 1) &ntilde;&euml;&aring;&auml;&oacute;&aring;&ograve; u = w = v . &Aring;&ntilde;&euml;&egrave; X &icirc;&iuml;&eth;&aring;&auml;&aring;&euml;&aring;&iacute;&icirc; &egrave;&ccedil; &ecirc;&agrave;&iacute;&icirc;&iacute;&egrave;&divide;&aring;&ntilde;&ecirc;&icirc;&eacute; &ccedil;&agrave;&auml;&agrave;&divide;&egrave;,
&ograve;.&aring;. X = {x | x &gt; 0, Ax = b}, &ograve;&icirc; &ograve;&icirc;&divide;&ecirc;&agrave; v &yuml;&acirc;&euml;&yuml;&aring;&ograve;&ntilde;&yuml; &oacute;&atilde;&euml;&icirc;&acirc;&icirc;&eacute; &ograve;&icirc;&atilde;&auml;&agrave; &egrave; &ograve;&icirc;&euml;&uuml;&ecirc;&icirc; &ograve;&icirc;&atilde;&auml;&agrave;, &ecirc;&icirc;&atilde;&auml;&agrave; &auml;&euml;&yuml; &iacute;&aring;&ecirc;&icirc;&ograve;&icirc;&eth;&ucirc;&otilde; j1 &lt; &middot; &middot; &middot; &lt; jr &acirc;&ucirc;&iuml;&icirc;&euml;&iacute;&aring;&iacute;&icirc; Aj1 vj1 + &middot; &middot; &middot; + Ajr vjr = b &egrave; vj = 0, j 6= jl ,
&atilde;&auml;&aring; r = rank A, &agrave; Aj1 , . . . , Ajr &euml;&egrave;&iacute;&aring;&eacute;&iacute;&icirc; &iacute;&aring;&ccedil;&agrave;&acirc;&egrave;&ntilde;&egrave;&igrave;&ucirc;&aring; &ntilde;&ograve;&icirc;&euml;&aacute;&ouml;&ucirc; &igrave;&agrave;&ograve;&eth;&egrave;&ouml;&ucirc; A. &Acirc; &yacute;&ograve;&icirc;&igrave;
&ntilde;&euml;&oacute;&divide;&agrave;&aring; &ntilde;&egrave;&ntilde;&ograve;&aring;&igrave;&oacute; Aj1 , . . . , Ajr &iacute;&agrave;&ccedil;&ucirc;&acirc;&agrave;&thorn;&ograve; &aacute;&agrave;&ccedil;&egrave;&ntilde;&icirc;&igrave; &oacute;&atilde;&euml;&icirc;&acirc;&icirc;&eacute; &ograve;&icirc;&divide;&ecirc;&egrave;, &agrave; vj1 , . . . , vjr &aacute;&agrave;&ccedil;&egrave;&ntilde;&iacute;&ucirc;&igrave;&egrave; &ecirc;&icirc;&icirc;&eth;&auml;&egrave;&iacute;&agrave;&ograve;&agrave;&igrave;&egrave;. &Aring;&ntilde;&euml;&egrave; &acirc;&ntilde;&aring; &aacute;&agrave;&ccedil;&egrave;&ntilde;&iacute;&ucirc;&aring; &ecirc;&icirc;&icirc;&eth;&auml;&egrave;&iacute;&agrave;&ograve;&ucirc; &iuml;&icirc;&euml;&icirc;&aelig;&egrave;&ograve;&aring;&euml;&uuml;&iacute;&ucirc;, &ograve;&icirc; &ograve;&icirc;&divide;&ecirc;&agrave; &iacute;&agrave;&ccedil;&ucirc;&acirc;&agrave;&aring;&ograve;&ntilde;&yuml;
&iacute;&aring;&acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&icirc;&eacute;, &egrave;&iacute;&agrave;&divide;&aring; &acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&icirc;&eacute;.
4. &Iuml;&oacute;&ntilde;&ograve;&uuml; X = {x | ha1 , xi 6 b, . . . , ham , xi 6 b}. &Auml;&icirc;&ecirc;&agrave;&aelig;&egrave;&ograve;&aring;, &divide;&ograve;&icirc; &ograve;&icirc;&divide;&ecirc;&agrave; &igrave;&iacute;&icirc;&aelig;&aring;&ntilde;&ograve;&acirc;&agrave;
&yuml;&acirc;&euml;&yuml;&aring;&ograve;&ntilde;&yuml; &oacute;&atilde;&euml;&icirc;&acirc;&icirc;&eacute; &ograve;&icirc;&atilde;&auml;&agrave; &egrave; &ograve;&icirc;&euml;&uuml;&ecirc;&icirc; &ograve;&icirc;&atilde;&auml;&agrave;, &ecirc;&icirc;&atilde;&auml;&agrave; &acirc; &iacute;&aring;&eacute; &icirc;&aacute;&eth;&agrave;&ugrave;&agrave;&thorn;&ograve;&ntilde;&yuml; &acirc; &ograve;&icirc;&divide;&iacute;&ucirc;&aring; &eth;&agrave;&acirc;&aring;&iacute;&ntilde;&ograve;&acirc;&agrave; &iacute;&aring;
&igrave;&aring;&iacute;&uuml;&oslash;&aring; n &iacute;&aring;&eth;&agrave;&acirc;&aring;&iacute;&ntilde;&ograve;&acirc; hai , xi 6 b, &ntilde;&eth;&aring;&auml;&egrave; &ecirc;&icirc;&ograve;&icirc;&eth;&ucirc;&otilde; n &euml;&egrave;&iacute;&aring;&eacute;&iacute;&icirc; &iacute;&aring;&ccedil;&agrave;&acirc;&egrave;&ntilde;&egrave;&igrave;&ucirc;&otilde;. &Ntilde;&ocirc;&icirc;&eth;&igrave;&oacute;&euml;&egrave;&eth;&oacute;&eacute;&ograve;&aring; &iuml;&icirc;&iacute;&yuml;&ograve;&egrave;&aring; &iacute;&aring;&acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&iacute;&icirc;&eacute; &ograve;&icirc;&divide;&ecirc;&egrave;, &ntilde;&icirc;&otilde;&eth;&agrave;&iacute;&yuml;&thorn;&ugrave;&aring;&aring;&ntilde;&yuml; &iuml;&eth;&egrave; &ntilde;&acirc;&aring;&auml;&aring;&iacute;&egrave;&egrave; &ecirc; &ecirc;&agrave;&iacute;&icirc;&iacute;&egrave;&divide;&aring;&ntilde;&ecirc;&icirc;&eacute; &ccedil;&agrave;&auml;&agrave;&divide;&aring;
&egrave; &auml;&icirc;&ecirc;&agrave;&aelig;&egrave;&ograve;&aring;, &divide;&ograve;&icirc; &ograve;&icirc;&divide;&ecirc;&agrave; &iacute;&aring;&acirc;&ucirc;&eth;&icirc;&aelig;&auml;&aring;&iacute;&agrave;, &aring;&ntilde;&euml;&egrave; &acirc; &eth;&agrave;&acirc;&aring;&iacute;&ntilde;&ograve;&acirc;&icirc; &icirc;&aacute;&eth;&agrave;&ugrave;&agrave;&thorn;&ograve;&ntilde;&yuml; &eth;&icirc;&acirc;&iacute;&icirc; n &iacute;&aring;&eth;&agrave;&acirc;&aring;&iacute;&ntilde;&ograve;&acirc;.
5. &Iacute;&agrave;&eacute;&auml;&egrave;&ograve;&aring; &acirc;&ntilde;&aring; &oacute;&atilde;&euml;&icirc;&acirc;&ucirc;&aring; &ograve;&icirc;&divide;&ecirc;&egrave; &egrave; &egrave;&otilde; &aacute;&agrave;&ccedil;&egrave;&ntilde;&ucirc; &auml;&euml;&yuml; &igrave;&iacute;&icirc;&aelig;&aring;&ntilde;&ograve;&acirc;:
a) X1 = {x ∈ R4 | x &gt; 0, x1 − 2x2 − x3 = 0, x1 + 3x2 + x4 = 1};
b) X2 = {x ∈ R5 | x &gt; 0, x1 + x2 + x3 + x4 = 1, −x1 + 2x2 + x3 + x5 = 1}
6. &Iuml;&eth;&egrave; &ecirc;&agrave;&ecirc;&egrave;&otilde; ai &egrave; b &igrave;&iacute;&icirc;&aelig;&aring;&ntilde;&ograve;&acirc;&icirc; {x | x &gt; 0, a1 x1 + &middot; &middot; &middot; + an xn = b} &iacute;&aring;&iuml;&oacute;&ntilde;&ograve;&icirc;? &Ntilde;&ecirc;&icirc;&euml;&uuml;&ecirc;&icirc;
&oacute;&atilde;&euml;&icirc;&acirc;&ucirc;&otilde; &ograve;&icirc;&divide;&aring;&ecirc; &icirc;&iacute;&icirc; &igrave;&icirc;&aelig;&aring;&ograve; &egrave;&igrave;&aring;&ograve;&uuml;?
7. &Auml;&icirc;&ecirc;&agrave;&aelig;&egrave;&ograve;&aring;, &divide;&ograve;&icirc; &acirc;&ntilde;&yuml;&ecirc;&agrave;&yuml; &oacute;&atilde;&euml;&icirc;&acirc;&agrave;&yuml; &ograve;&icirc;&divide;&ecirc;&agrave; &auml;&euml;&yuml; &igrave;&iacute;&icirc;&aelig;&aring;&ntilde;&ograve;&acirc;&agrave; {x | x &gt; 0, Ax = b} &yuml;&acirc;&euml;&yuml;&aring;&ograve;&ntilde;&yuml;
&oacute;&atilde;&euml;&icirc;&acirc;&icirc;&eacute; &egrave; &auml;&euml;&yuml; &igrave;&iacute;&icirc;&aelig;&aring;&ntilde;&ograve;&acirc;&agrave; {x | x &gt; 0, Ax 6 b}.
```