Problemi LP con due variabili – Tipo C¶

Catalogo dei problemi · Catalogo dei problemi (PDF)

Problema LP \(P21\)¶

\[ \begin{array}{rrrrrrrrrrrrr} {\max} & \, {x_1} & {+} & {2}\, {x_2} \\[2ex] \text{soggetto a} & {-}\, {x_1} & {-} & \, {x_2} & {\le} & {-2} \\[1.5ex] & {4}\, {x_1} & {-} & {2}\, {x_2} & {\le} & {7} \\[1.5ex] & \, {x_1} & {+} & {5}\, {x_2} & {\le} & {21} \\[1.5ex] & {x_1,} & & {x_2} & { \ge} & { 0 } \end{array} \]

Figura 1

Problema LP \(P22\)¶

\[ \begin{array}{rrrrrrrrrrrrr} {\max} & {3}\, {x_1} & {+} & \, {x_2} \\[2ex] \text{soggetto a} & \, {x_1} & {-} & \, {x_2} & {\le} & {-1} \\[1.5ex] & {-}\, {x_1} & {-} & \, {x_2} & {\le} & {-3} \\[1.5ex] & {2}\, {x_1} & {+} & \, {x_2} & {\le} & {4} \\[1.5ex] & {x_1,} & & {x_2} & { \ge} & { 0 } \end{array} \]

Figura 2

Problema LP \(P23\)¶

\[ \begin{array}{rrrrrrrrrrrrr} {\max} & \, {x_1} & {+} & {4}\, {x_2} \\[2ex] \text{soggetto a} & {3}\, {x_1} & {+} & {8}\, {x_2} & {\le} & {24} \\[1.5ex] & \, {x_1} & & & {\ge} & {1} \\[1.5ex] & & & \, {x_2} & {\ge} & {1} \\[1.5ex] & {x_1,} & & {x_2} & { \ge} & { 0 } \end{array} \]

Figura 3

Problema LP \(P24\)¶

\[ \begin{array}{rrrrrrrrrrrrr} {\max} & {4}\, {x_1} & {+} & {3}\, {x_2} \\[2ex] \text{soggetto a} & {7}\, {x_1} & {+} & {3}\, {x_2} & {\le} & {24} \\[1.5ex] & {-}\, {x_1} & {+} & \, {x_2} & {\le} & {3} \\[1.5ex] & \, {x_1} & & & {\ge} & {1} \\[1.5ex] & & & \, {x_2} & {\ge} & {2} \\[1.5ex] & {x_1,} & & {x_2} & { \ge} & { 0 } \end{array} \]

Figura 4

Problema LP \(P25\)¶

\[ \begin{array}{rrrrrrrrrrrrr} {\max} & {2}\, {x_1} & {+} & {2}\, {x_2} \\[2ex] \text{soggetto a} & \, {x_1} & & & {\ge} & {1} \\[1.5ex] & & & \, {x_2} & {\le} & {3} \\[1.5ex] & {2}\, {x_1} & {-} & \, {x_2} & {\le} & {7} \\[1.5ex] & {x_1,} & & {x_2} & { \ge} & { 0 } \end{array} \]

Figura 5

Problema LP \(P26\)¶

\[ \begin{array}{rrrrrrrrrrrrr} {\max} & {2}\, {x_1} & {+} & {3}\, {x_2} \\[2ex] \text{soggetto a} & {-}\, {x_1} & {-} & \, {x_2} & {\le} & {-2} \\[1.5ex] & \, {x_1} & {+} & {2}\, {x_2} & {\le} & {8} \\[1.5ex] & {3}\, {x_1} & {+} & \, {x_2} & {\le} & {9} \\[1.5ex] & {x_1,} & & {x_2} & { \ge} & { 0 } \end{array} \]

Figura 6

Problema LP \(P27\)¶

\[ \begin{array}{rrrrrrrrrrrrr} {\max} & {2}\, {x_1} & {+} & \, {x_2} \\[2ex] \text{soggetto a} & \, {x_1} & {+} & \, {x_2} & {\le} & {8} \\[1.5ex] & {2}\, {x_1} & {-} & {2}\, {x_2} & {\le} & {4} \\[1.5ex] & {-}{2}\, {x_1} & {+} & \, {x_2} & {\le} & {-1} \\[1.5ex] & {x_1,} & & {x_2} & { \ge} & { 0 } \end{array} \]

Figura 7

Problema LP \(P28\)¶

\[ \begin{array}{rrrrrrrrrrrrr} {\max} & {3}\, {x_1} & {+} & {2}\, {x_2} \\[2ex] \text{soggetto a} & \, {x_1} & {+} & \, {x_2} & {\le} & {6} \\[1.5ex] & {-}{2}\, {x_1} & {-} & \, {x_2} & {\le} & {-4} \\[1.5ex] & & & \, {x_2} & {\le} & {3} \\[1.5ex] & {x_1,} & & {x_2} & { \ge} & { 0 } \end{array} \]

Figura 8

Problema LP \(P29\)¶

\[ \begin{array}{rrrrrrrrrrrrr} {\max} & {3}\, {x_1} & {+} & \, {x_2} \\[2ex] \text{soggetto a} & {-}\, {x_1} & {+} & {2}\, {x_2} & {\le} & {2} \\[1.5ex] & & & \, {x_2} & {\ge} & {1} \\[1.5ex] & \, {x_1} & & & {\le} & {5} \\[1.5ex] & {x_1,} & & {x_2} & { \ge} & { 0 } \end{array} \]

Figura 9

Problema LP \(P30\)¶

\[ \begin{array}{rrrrrrrrrrrrr} {\max} & \, {x_1} & {+} & \, {x_2} \\[2ex] \text{soggetto a} & {-}\, {x_1} & {+} & \, {x_2} & {\le} & {2} \\[1.5ex] & {-}\, {x_1} & {-} & {2}\, {x_2} & {\le} & {-4} \\[1.5ex] & {2}\, {x_1} & {-} & \, {x_2} & {\le} & {8} \\[1.5ex] & & & {2}\, {x_2} & {\le} & {8} \\[1.5ex] & {x_1,} & & {x_2} & { \ge} & { 0 } \end{array} \]

Figura 10