LP problems with two variables – Type C¶
Catalogue of LP problems · Problem catalogue (PDF)
LP Problem \(P21\)¶
\[
\begin{array}{rrrrrrrrrrrrr}
{\max} & \, {x_1} & {+} & {2}\, {x_2} \\[2ex]
\text{subject to} & {-}\, {x_1} & {-} & \, {x_2} & {\le} & {-2} \\[1.5ex]
& {4}\, {x_1} & {-} & {2}\, {x_2} & {\le} & {7} \\[1.5ex]
& \, {x_1} & {+} & {5}\, {x_2} & {\le} & {21} \\[1.5ex]
& {x_1,} & & {x_2} & { \ge} & { 0 }
\end{array}
\]
LP Problem \(P22\)¶
\[
\begin{array}{rrrrrrrrrrrrr}
{\max} & {3}\, {x_1} & {+} & \, {x_2} \\[2ex]
\text{subject to} & \, {x_1} & {-} & \, {x_2} & {\le} & {-1} \\[1.5ex]
& {-}\, {x_1} & {-} & \, {x_2} & {\le} & {-3} \\[1.5ex]
& {2}\, {x_1} & {+} & \, {x_2} & {\le} & {4} \\[1.5ex]
& {x_1,} & & {x_2} & { \ge} & { 0 }
\end{array}
\]
LP Problem \(P23\)¶
\[
\begin{array}{rrrrrrrrrrrrr}
{\max} & \, {x_1} & {+} & {4}\, {x_2} \\[2ex]
\text{subject to} & {3}\, {x_1} & {+} & {8}\, {x_2} & {\le} & {24} \\[1.5ex]
& \, {x_1} & & & {\ge} & {1} \\[1.5ex]
& & & \, {x_2} & {\ge} & {1} \\[1.5ex]
& {x_1,} & & {x_2} & { \ge} & { 0 }
\end{array}
\]
LP Problem \(P24\)¶
\[
\begin{array}{rrrrrrrrrrrrr}
{\max} & {4}\, {x_1} & {+} & {3}\, {x_2} \\[2ex]
\text{subject to} & {7}\, {x_1} & {+} & {3}\, {x_2} & {\le} & {24} \\[1.5ex]
& {-}\, {x_1} & {+} & \, {x_2} & {\le} & {3} \\[1.5ex]
& \, {x_1} & & & {\ge} & {1} \\[1.5ex]
& & & \, {x_2} & {\ge} & {2} \\[1.5ex]
& {x_1,} & & {x_2} & { \ge} & { 0 }
\end{array}
\]
LP Problem \(P25\)¶
\[
\begin{array}{rrrrrrrrrrrrr}
{\max} & {2}\, {x_1} & {+} & {2}\, {x_2} \\[2ex]
\text{subject to} & \, {x_1} & & & {\ge} & {1} \\[1.5ex]
& & & \, {x_2} & {\le} & {3} \\[1.5ex]
& {2}\, {x_1} & {-} & \, {x_2} & {\le} & {7} \\[1.5ex]
& {x_1,} & & {x_2} & { \ge} & { 0 }
\end{array}
\]
LP Problem \(P26\)¶
\[
\begin{array}{rrrrrrrrrrrrr}
{\max} & {2}\, {x_1} & {+} & {3}\, {x_2} \\[2ex]
\text{subject to} & {-}\, {x_1} & {-} & \, {x_2} & {\le} & {-2} \\[1.5ex]
& \, {x_1} & {+} & {2}\, {x_2} & {\le} & {8} \\[1.5ex]
& {3}\, {x_1} & {+} & \, {x_2} & {\le} & {9} \\[1.5ex]
& {x_1,} & & {x_2} & { \ge} & { 0 }
\end{array}
\]
LP Problem \(P27\)¶
\[
\begin{array}{rrrrrrrrrrrrr}
{\max} & {2}\, {x_1} & {+} & \, {x_2} \\[2ex]
\text{subject to} & \, {x_1} & {+} & \, {x_2} & {\le} & {8} \\[1.5ex]
& {2}\, {x_1} & {-} & {2}\, {x_2} & {\le} & {4} \\[1.5ex]
& {-}{2}\, {x_1} & {+} & \, {x_2} & {\le} & {-1} \\[1.5ex]
& {x_1,} & & {x_2} & { \ge} & { 0 }
\end{array}
\]
LP Problem \(P28\)¶
\[
\begin{array}{rrrrrrrrrrrrr}
{\max} & {3}\, {x_1} & {+} & {2}\, {x_2} \\[2ex]
\text{subject to} & \, {x_1} & {+} & \, {x_2} & {\le} & {6} \\[1.5ex]
& {-}{2}\, {x_1} & {-} & \, {x_2} & {\le} & {-4} \\[1.5ex]
& & & \, {x_2} & {\le} & {3} \\[1.5ex]
& {x_1,} & & {x_2} & { \ge} & { 0 }
\end{array}
\]
LP Problem \(P29\)¶
\[
\begin{array}{rrrrrrrrrrrrr}
{\max} & {3}\, {x_1} & {+} & \, {x_2} \\[2ex]
\text{subject to} & {-}\, {x_1} & {+} & {2}\, {x_2} & {\le} & {2} \\[1.5ex]
& & & \, {x_2} & {\ge} & {1} \\[1.5ex]
& \, {x_1} & & & {\le} & {5} \\[1.5ex]
& {x_1,} & & {x_2} & { \ge} & { 0 }
\end{array}
\]
LP Problem \(P30\)¶
\[
\begin{array}{rrrrrrrrrrrrr}
{\max} & \, {x_1} & {+} & \, {x_2} \\[2ex]
\text{subject to} & {-}\, {x_1} & {+} & \, {x_2} & {\le} & {2} \\[1.5ex]
& {-}\, {x_1} & {-} & {2}\, {x_2} & {\le} & {-4} \\[1.5ex]
& {2}\, {x_1} & {-} & \, {x_2} & {\le} & {8} \\[1.5ex]
& & & {2}\, {x_2} & {\le} & {8} \\[1.5ex]
& {x_1,} & & {x_2} & { \ge} & { 0 }
\end{array}
\]
