Problemi LP con due variabili – Tipo D¶

Catalogo dei problemi · Catalogo dei problemi (PDF)

Problema LP \(P31\)¶

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

Figura 1

Problema LP \(P32\)¶

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

Figura 2

Problema LP \(P33\)¶

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

Figura 3

Problema LP \(P34\)¶

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

Figura 4

Problema LP \(P35\)¶

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

Figura 5

Problema LP \(P36\)¶

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

Figura 6

Problema LP \(P37\)¶

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

Figura 7

Problema LP \(P38\)¶

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

Figura 8

Problema LP \(P39\)¶

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

Figura 9

Problema LP \(P40\)¶

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

Figura 10