1-definitions_ex.Rmd

## Exercises {-}

1. Determine all values of \(a\) such that the problem
\[
\begin{array}{rl}
\min & x + y \\
\text{s.t.} 
&  -3x + y \geq a \\
&  2x - y \geq 0 \\
& x + 2y \geq 2
\end{array}
\]
is infeasible.

2. Show that the problem
\[
\begin{array}{rl}
\min & 2^x \cdot 4^y \\
\text{s.t.} 
&  e^{-3x + y} \geq 1 \\
&  |2x - y| \leq 4 \\
\end{array}
\]
can be solved by solving a linear programming problem.