Problemi LP con due variabili – Tipo B¶

Catalogo dei problemi · Catalogo dei problemi (PDF)

Problema LP \(P11\)¶

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

Figura 1

Problema LP \(P12\)¶

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

Figura 2

Problema LP \(P13\)¶

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

Figura 3

Problema LP \(P14\)¶

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

Figura 4

Problema LP \(P15\)¶

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

Figura 5

Problema LP \(P16\)¶

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

Figura 6

Problema LP \(P17\)¶

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

Figura 7

Problema LP \(P18\)¶

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

Figura 8

Problema LP \(P19\)¶

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

Figura 9

Problema LP \(P20\)¶

\[ \begin{array}{rrrrrrrrrrrrr} {\max} & {-}{3}\, {x_1} & {-} & \, {x_2} \\[2ex] \text{soggetto a} & \, {x_1} & {-} & \, {x_2} & {\le} & {5} \\[1.5ex] & {-}{2}\, {x_1} & {-} & \, {x_2} & {\le} & {-4} \\[1.5ex] & {x_1,} & & {x_2} & { \ge} & { 0 } \end{array} \]

Figura 10