Problemi LP con tre variabili – Tipo A¶

Catalogo dei problemi · Catalogo dei problemi (PDF)

Problema LP \(P41\)¶

\[ \begin{array}{rrrrrrrrrrrrr} {\max} & 2\; {x_1} & {+} & {x_2} & {+} & 3\; {x_3} \\[1.5ex] \text{soggetto a} & \, {x_1} & {+} & \, {x_2} & {+} & \, {x_3} & {\le} & {4} \\[1.5ex] & & & \, {x_2} & & & {\le} & {2} \\[1.5ex] & & & & & \, {x_3} & {\le} & {3} \\[1.5ex] & 3\, {x_1} & & & {+} & \, {x_3} & {\le} & {6} \\[1.5ex] & {x_1,} & & {x_2,} & & {x_3} & { \ge} & { 0 } \end{array} \]

Figura 1

Problema LP \(P42\)¶

\[ \begin{array}{rrrrrrrrrrrrr} {\max} & 3 \, {x_1} & {+} & 2 \, {x_2} & {+} & 4 \, {x_3} \\[2ex] \text{soggetto a} & \, {x_1} & {+} & \, {x_2} & {+} & 2 \, {x_3} & {\le} & 4 \\[2ex] & 2 \, {x_1} & & & {+} & 3 \, {x_3} & {\le} & 5 \\[2ex] & 2 \, {x_1} & {+} & \, {x_2} & {+} & 3 \, {x_3} & {\le} & 7 \\[2ex] & {x_1,} & & {x_2,} & & \, {x_3} & { \ge} & { 0 } \end{array} \]

Figura 2

Problema LP \(P43\)¶

\[ \begin{array}{rrrrrrrrrrrrr} {\max} & {x_1} & {+} & 2 \, {x_2} & {+} & 7 \, {x_3} \\[2ex] \text{soggetto a} & {x_1} & & & {+} & 2 \, {x_3} & {\le} & 2 \\[2ex] & & & {x_2} & {+} & 2 \, {x_3} & {\le} & 2 \\[2ex] & {x_1,} & & {x_2,} & & {x_3} & { \ge} & {0} \end{array} \]

Figura 3

Problema LP \(P44\)¶

\[ \begin{array}{rrrrrrrrrrrrr} {\max} & {x_1} & {+} & 2 \, {x_2} & {+} & 3 \, {x_3} \\[2ex] \text{soggetto a} & {x_1} & {+} & 2 \, {x_2} & {-} & 2 \, {x_3} & {\le} & 1 \\[2ex] & 2 \, {x_1} & {-} & \, {x_2} & {-} & 3 \, {x_3} & {\le} & 4 \\[2ex] & {x_1} & {+} & 2 \, {x_2} & {+} & 5 \, {x_3} & {\le} & 2 \\[2ex] & {x_1,} & & {x_2,} & & \, {x_3} & {\ge} & { 0 } \end{array} \]

Figura 4

Problema LP \(P45\)¶

\[ \begin{array}{rrrrrrrrrrrrr} {\max} & {4} \, {x_1} & {-} & 13\, {x_2} & {+} & {7} \, {x_3} \\[1.5ex] \text{soggetto a} & 3\, {x_1} & {+} & 2 \, {x_2} & {+} & 5 \, {x_3} & {\le} & {5} \\[1.5ex] & {x_1} & {-} & 3\, {x_2} & {+} & 5\, {x_3} & {\le} & {3} \\[1.5ex] & {x_1,} & & {x_2,} & & {x_3} & { \ge} & { 0 } \end{array} \]

Figura 5

Problema LP \(P46\)¶

\[ \begin{array}{rrrrrrrrrrrrr} {\max} & 5\, {x_1} & {+} & 6\, {x_2} & {+} & 10\, {x_3} \\[2ex] \text{soggetto a} & 9\, {x_1} & {+} & 2 \, {x_2} & {+} & 2\, {x_3} & {\le} & 11 \\[2ex] & 2\, {x_1} & {+} & 6 \, {x_2} & {+} & 6\, {x_3} & {\le} & 16 \\[2ex] & 4\, {x_1} & {+} & 2 \, {x_2} & {+} & 7\, {x_3} & {\le} & 10 \\[2ex] & {x_1}, & & {x_2}, & & {x_3} & {\ge} & { 0 } \end{array} \]

Figura 6