Problemi LP con tre variabili – Tipo C¶

Catalogo dei problemi · Catalogo dei problemi (PDF)

Problema LP \(P61\)¶

\[ \begin{array}{rrrrrrrrrrrrrrrr} {\max} & & {3\,x_1} & {+} & {\,x_2} & {+} & {2\,x_3} & & \\[2ex] \text{soggetto a} & & {\,x_1} & & & {+} & {\,x_3} & {\le} & {5} \\[2ex] & {-} & {\,x_1} & & & {-} & {\,x_3} & {\le} & {-4} \\[2ex] & {-} & {\,x_1} & {+} & {2\,x_2} & {+} & {\,x_3} & {\le} & {5} \\[2ex] & & {x_1,} & & {x_2,} & & {x_3} & { \ge} & { 0 } \end{array} \]

Figura 1

Problema LP \(P62\)¶

\[ \begin{array}{rrrrrrrrrrrrrrrr} {\max} & & {2\,x_1} & {+} & {3\,x_2} & {+} & {\,x_3} & & \\[2ex] \text{soggetto a} & & & & {\,x_2} & {+} & {\,x_3} & {\le} & {6} \\[2ex] & {-} & {2\,x_1} & {-} & {\,x_2} & {-} & {\,x_3} & {\le} & {-2} \\[2ex] & & {2\,x_1} & & & {-} & {\,x_3} & {\le} & {4} \\[2ex] & & {x_1,} & & {x_2,} & & {x_3} & { \ge} & { 0 } \end{array} \]

Figura 2

Problema LP \(P63\)¶

\[ \begin{array}{rrrrrrrrrrrrrrrr} {\max} & & {\,x_1} & {+} & {2\,x_2} & {+} & {2\,x_3} & & \\[2ex] \text{soggetto a} & & {\,x_1} & {+} & {\,x_2} & & & {\le} & {4} \\[2ex] & & {\,x_1} & {+} & {2\,x_2} & {-} & {\,x_3} & {\le} & {6} \\[2ex] & {-} & {2\,x_1} & {-} & {2\,x_2} & {+} & {\,x_3} & {\le} & {-3} \\[2ex] & & {x_1,} & & {x_2,} & & {x_3} & { \ge} & { 0 } \end{array} \]

Figura 3

Problema LP \(P64\)¶

\[ \begin{array}{rrrrrrrrrrrrrrrr} {\max} & & {3\,x_1} & {+} & {2\,x_2} & {+} & {\,x_3} & & \\[2ex] \text{soggetto a} & {-} & {\,x_1} & {-} & {2\,x_2} & {-} & {2\,x_3} & {\le} & {-3} \\[2ex] & & {\,x_1} & {+} & {\,x_2} & {+} & {\,x_3} & {\le} & {5} \\[2ex] & & & & {\,x_2} & {-} & {\,x_3} & {\le} & {2} \\[2ex] & & {x_1,} & & {x_2,} & & {x_3} & { \ge} & { 0 } \end{array} \]

Figura 4

Problema LP \(P65\)¶

\[ \begin{array}{rrrrrrrrrrrrrrrr} {\max} & & {2\,x_1} & {+} & {3\,x_2} & {+} & {3\,x_3} & & \\[2ex] \text{soggetto a} & & {\,x_1} & {+} & {\,x_2} & & & {\le} & {5} \\[2ex] & & {2\,x_1} & {-} & {\,x_2} & & & {\le} & {4} \\[2ex] & {-} & {2\,x_1} & {-} & {\,x_2} & {+} & {\,x_3} & {\le} & {-3} \\[2ex] & & {x_1,} & & {x_2,} & & {x_3} & { \ge} & { 0 } \end{array} \]

Figura 5

Problema LP \(P66\)¶

\[ \begin{array}{rrrrrrrrrrrrrrrr} {\max} & & {2\,x_1} & {+} & {\,x_2} & {+} & {\,x_3} & & \\[2ex] \text{soggetto a} & {-} & {2\,x_1} & {+} & {\,x_2} & {-} & {2\,x_3} & {\le} & {-3} \\[2ex] & & {\,x_1} & & & {+} & {\,x_3} & {\le} & {3} \\[2ex] & {-} & {2\,x_1} & {+} & {2\,x_2} & & & {\le} & {2} \\[2ex] & & {x_1,} & & {x_2,} & & {x_3} & { \ge} & { 0 } \end{array} \]

Figura 6