Finding feasible solution s.t. value of objective function is greater than $248$.

Question

I was asked the following question in examination :

Using the simplex method ,verify that following problem is unbounded

and hence find a feasible solution for which the value of the following objective function is greater than $248.$ :

maximize :

$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~2x_1+3x_2$ subject to ,

$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x_1-x_2+x_3\leq 2$

$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-3x_1+x_2\leq4$ ,$~~~~~~~~~x_1,x_2\geq0$

I got how to show unboundedness,but can't get how to find a feasible sol$^n$ for which value of objective function is greater than $248.$

Kindly help ..

Answer 1

If you choose $x_1=x_2=t$ and $x_3=0$, then the value of the objective function will be equal to $5t$, and all the constraint will be satisfied. So if you need greater value than $248$, then it is enough to choose $t > 248/5$.