Question

Consider the following IP problem:

Answer 1

Answer:

$(3,0)$

Step-by-step explanation:

The integer points which fall in the common region bounded by the lines are

$(0,2),(2,3),(3,0)$

Since, one of the points is $(2.22...,3.11....)$ we round it to $(2,3)$

If we round up then the point will be $(3,4)$ which does not fall in the bounded region.

Also $x_1\geq 0$ and $x_2\geq 0$ no negative values are considered.

Applying in the values in the LP problem $Z=5x_1+x_2$

$Z=5\times 0+2\\\Rightarrow Z=2$

$Z=5\times 2+3\\\Rightarrow Z=13$

$Z=5\times 3+0\\\Rightarrow Z=15$

So, the LP problem is maximum at point $(3,0)$.