I was first asked to solve the following linear program:
$Z_{max}=2x+3y$
subject to the constraints
$\begin{align*} &2x+7y\ge22\\ &x+y\ge6 \\ &5x+y\ge10 \\ &x,y\ge0 \end{align*}$
I solved it graphically and found that the feasible region is unbounded. Next I was asked to justify:
Any objective function of the form $lx-my$ (both $l, m$ of same sign) has finite maximum or infinite minimum subject to the constraints of the above LPP.
Since the feasible region is unbounded above, so infinite maximum is a possible case. Again since the region is bounded below, so the minimum value is finite and corresponds to the vertex $(4,2)$.
I don't get the sense of this question. Neither "Finite maximum" nor "Infinite minimum" is a possibility subject to the given constraints. Because here maximum is infinite and minimum is finite.
Nevertheless if the statement is valid, what would be correct justification?