Problemi LP con tre variabili – Tipo B¶

Catalogo dei problemi · Catalogo dei problemi (PDF)

Problema LP \(P51\)¶

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

Figura 1

Problema LP \(P52\)¶

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

Figura 2

Problema LP \(P53\)¶

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

Figura 3

Problema LP \(P54\)¶

\[ \begin{array}{rrrrrrrrrrrrrrrr} {\max} & {-} & {\,x_1} & {-} & {2\,x_2} & {-} & {2\,x_3} & & \\[2ex] \text{soggetto a} & & {\,x_1} & {+} & {2\,x_2} & & & {\le} & {6} \\[2ex] & {-} & {\,x_1} & {-} & {\,x_2} & {-} & {\,x_3} & {\le} & {-3} \\[2ex] & & & & {\,x_2} & {+} & {\,x_3} & {\le} & {5} \\[2ex] & & {x_1,} & & {x_2,} & & {x_3} & { \ge} & { 0 } \end{array} \]

Figura 4

Problema LP \(P55\)¶

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

Figura 5

Problema LP \(P56\)¶

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

Figura 6