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# True or False: In a LPP,the maximum value of the objective function $Z=ax+by$ is always finite.

Can you answer this question?

Toolbox:
• The objective function $Z=ax+by$,where $a$ and $b$ constants,which has to be minimized or maximized.
Step 1:
If $M$ is the maximum value of $Z$,if the open half plane determinant by $ax+by$ > $M$ has no point in common with the feasible region.Otherwise $Z$ has no maximum value.
Step 2:
In a LPP,the maximum value of the objective function $Z=ax+by$ is always finite.
Hence it is a True statement.
answered Aug 28, 2013