Problemi LP con due variabili – Tipo A¶

Catalogo dei problemi · Catalogo dei problemi (PDF)

Problema LP \(P0\)¶

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

Figura 1

Problema LP \(P1\)¶

\[ \begin{array}{rrrrrrrrrrrrr} {\max} & {x_1} & {+} & 8 \, {x_2} \\[2ex] \text{soggetto a} & {3} \, {x_1} & {+} & {6} \, {x_2} & {\le} & {16} \\[2ex] & {x_1,} & & {x_2} & { \ge} & {0 } \end{array} \]

Figura 2

Problema LP \(P2\)¶

\[ \begin{array}{rrrrrrrrrrrrr} {\max} & {x_1} & {+} & 3 \, {x_2} \\[2ex] \text{soggetto a} & {-}4 \, {x_1} & {+} & 10 \, {x_2} & {\le} & 35 \\[2ex] & 3 \, {x_1} & {+} & \, {x_2} & {\le} & 12 \\[2ex] & {x_1,} & & {x_2} & { \ge} & { 0 } \end{array} \]

Figura 3

Problema LP \(P3\)¶

\[ \begin{array}{rrrrrrrrrrrrr} {\max} & {2} \, {x_1} & {+} & {4} \, {x_2} \\[2ex] \text{soggetto a} & {-} \, {x_1} & {+} & \, {x_2} & {\le} & {2} \\[2ex] & {8} \, {x_1} & {+} & {2} \, {x_2} & {\le} & {19} \\[2ex] & {x_1,} & & {x_2} & { \ge} & { 0 } \end{array} \]

Figura 4

Problema LP \(P4\)¶

\[ \begin{array}{rrrrrrrrrrrrr} {\max} & 5 {x_1} & {+} & 3 \, {x_2} \\[2ex] \text{soggetto a} & 2 \, {x_1} & {+} & \, {x_2} & {\le} & 14 \\[2ex] & \, {x_1} & {+} & 8 \, {x_2} & {\le} & 32 \\[2ex] & {x_1,} & & {x_2} & { \ge} & { 0 } \end{array} \]

Figura 5

Problema LP \(P5\)¶

\[ \begin{array}{rrrrrrrrrrrrr} {\max} & 2 {x_1} & {+} & 3 \, {x_2} \\[2ex] \text{soggetto a} & 6 \, {x_1} & {+} & 21 \, {x_2} & {\le} & 77 \\[2ex] & 8 \, {x_1} & {+} & 3 \, {x_2} & {\le} & 36 \\[2ex] & {x_1,} & & {x_2} & { \ge} & { 0 } \end{array} \]

Figura 6

Problema ILP \(P6\)¶

\[ \begin{array}{rrrrrrrrrrrrr} {\max} & {x_1} & {+} & \, {x_2} \\[2ex] \text{soggetto a} & {4} \, {x_1} & {+} & {15} \, {x_2} & {\le} & {70} \\[2ex] & {12} \, {x_1} & {+} & {3} \, {x_2} & {\le} & {52} \\[2ex] & {x_1,} & & {x_2} & {\in} & {\mathbb{Z}_{\ge 0}} \end{array} \]

Figura 7

Problema LP \(P7\)¶

\[ \begin{array}{rrrrrrrrrrrrr} {\max} & 3 \, {x_1} & {+} & {x_2} \\[2ex] \text{soggetto a} & {x_1} & {+} & {4} \, {x_2} & {\le} & {12} \\[2ex] & 2 \, {x_1} & {+} & \, {x_2} & {\le} & 5 \\[2ex] & {x_1,} & & {x_2} & {\ge} & {0} \end{array} \]

Figura 8

Problema LP \(P8\)¶

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

Figura 9

Problema LP \(P9\)¶

\[ \begin{array}{rrrrrrrrrrrrr} {\max} & 2 \, {x_1} & {+} & {x_2} \\[2ex] \text{soggetto a} & {-} \, {x_1} & {+} & \, {x_2} & {\le} & 1 \\[2ex] & {6} \, {x_1} & {+} & {4} \, {x_2} & {\le} & {39} \\[2ex] & {x_1,} & & {x_2} & { \ge} & {0} \end{array} \]

Figura 10

Problema LP \(P10\)¶

\[ \begin{array}{rrrrrrrrrrrrr} {\max} & 5 \, {x_1} & {+} & 2 \, {x_2} \\[2ex] \text{soggetto a} & {-} \, {x_1} & {+} & 3 \, {x_2} & {\le} & 12 \\[2ex] & {x_1} & {+} & 2 \, {x_2} & {\le} & 12 \\[2ex] & {3} \, {x_1} & {-} & 2 \, {x_2} & {\le} & {8} \\[2ex] & {x_1,} & & {x_2} & { \ge} & {0} \end{array} \]

Figura 11