Skip to content

LP problems with two variables – Type B

Catalogue of LP problems · Problem catalogue (PDF)

LP Problem \(P11\)

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

Figure 1

LP Problem \(P12\)

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

Figure 2

LP Problem \(P13\)

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

Figure 3

LP Problem \(P14\)

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

Figure 4

LP Problem \(P15\)

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

Figure 5

LP Problem \(P16\)

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

Figure 6

LP Problem \(P17\)

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

Figure 7

LP Problem \(P18\)

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

Figure 8

LP Problem \(P19\)

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

Figure 9

LP Problem \(P20\)

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

Figure 10