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LP problems with two variables – Type D

Catalogue of LP problems · Problem catalogue (PDF)

LP Problem \(P31\)

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

Figure 1

LP Problem \(P32\)

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

Figure 2

LP Problem \(P33\)

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

Figure 3

LP Problem \(P34\)

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

Figure 4

LP Problem \(P35\)

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

Figure 5

LP Problem \(P36\)

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

Figure 6

LP Problem \(P37\)

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

Figure 7

LP Problem \(P38\)

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

Figure 8

LP Problem \(P39\)

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

Figure 9

LP Problem \(P40\)

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

Figure 10