LP problems with three variables – Type C¶
Catalogue of LP problems · Problem catalogue (PDF)
LP Problem \(P61\)¶
\[
\begin{array}{rrrrrrrrrrrrrrrr}
{\max} & & {3\,x_1} & {+} & {\,x_2} & {+} & {2\,x_3} & & \\[2ex]
\text{subject to} & & {\,x_1} & & & {+} & {\,x_3} & {\le} & {5} \\[2ex]
& {-} & {\,x_1} & & & {-} & {\,x_3} & {\le} & {-4} \\[2ex]
& {-} & {\,x_1} & {+} & {2\,x_2} & {+} & {\,x_3} & {\le} & {5} \\[2ex]
& & {x_1,} & & {x_2,} & & {x_3} & { \ge} & { 0 }
\end{array}
\]
LP Problem \(P62\)¶
\[
\begin{array}{rrrrrrrrrrrrrrrr}
{\max} & & {2\,x_1} & {+} & {3\,x_2} & {+} & {\,x_3} & & \\[2ex]
\text{subject to} & & & & {\,x_2} & {+} & {\,x_3} & {\le} & {6} \\[2ex]
& {-} & {2\,x_1} & {-} & {\,x_2} & {-} & {\,x_3} & {\le} & {-2} \\[2ex]
& & {2\,x_1} & & & {-} & {\,x_3} & {\le} & {4} \\[2ex]
& & {x_1,} & & {x_2,} & & {x_3} & { \ge} & { 0 }
\end{array}
\]
LP Problem \(P63\)¶
\[
\begin{array}{rrrrrrrrrrrrrrrr}
{\max} & & {\,x_1} & {+} & {2\,x_2} & {+} & {2\,x_3} & & \\[2ex]
\text{subject to} & & {\,x_1} & {+} & {\,x_2} & & & {\le} & {4} \\[2ex]
& & {\,x_1} & {+} & {2\,x_2} & {-} & {\,x_3} & {\le} & {6} \\[2ex]
& {-} & {2\,x_1} & {-} & {2\,x_2} & {+} & {\,x_3} & {\le} & {-3} \\[2ex]
& & {x_1,} & & {x_2,} & & {x_3} & { \ge} & { 0 }
\end{array}
\]
LP Problem \(P64\)¶
\[
\begin{array}{rrrrrrrrrrrrrrrr}
{\max} & & {3\,x_1} & {+} & {2\,x_2} & {+} & {\,x_3} & & \\[2ex]
\text{subject to} & {-} & {\,x_1} & {-} & {2\,x_2} & {-} & {2\,x_3} & {\le} & {-3} \\[2ex]
& & {\,x_1} & {+} & {\,x_2} & {+} & {\,x_3} & {\le} & {5} \\[2ex]
& & & & {\,x_2} & {-} & {\,x_3} & {\le} & {2} \\[2ex]
& & {x_1,} & & {x_2,} & & {x_3} & { \ge} & { 0 }
\end{array}
\]
LP Problem \(P65\)¶
\[
\begin{array}{rrrrrrrrrrrrrrrr}
{\max} & & {2\,x_1} & {+} & {3\,x_2} & {+} & {3\,x_3} & & \\[2ex]
\text{subject to} & & {\,x_1} & {+} & {\,x_2} & & & {\le} & {5} \\[2ex]
& & {2\,x_1} & {-} & {\,x_2} & & & {\le} & {4} \\[2ex]
& {-} & {2\,x_1} & {-} & {\,x_2} & {+} & {\,x_3} & {\le} & {-3} \\[2ex]
& & {x_1,} & & {x_2,} & & {x_3} & { \ge} & { 0 }
\end{array}
\]
LP Problem \(P66\)¶
\[
\begin{array}{rrrrrrrrrrrrrrrr}
{\max} & & {2\,x_1} & {+} & {\,x_2} & {+} & {\,x_3} & & \\[2ex]
\text{subject to} & {-} & {2\,x_1} & {+} & {\,x_2} & {-} & {2\,x_3} & {\le} & {-3} \\[2ex]
& & {\,x_1} & & & {+} & {\,x_3} & {\le} & {3} \\[2ex]
& {-} & {2\,x_1} & {+} & {2\,x_2} & & & {\le} & {2} \\[2ex]
& & {x_1,} & & {x_2,} & & {x_3} & { \ge} & { 0 }
\end{array}
\]
