The objective function $z=x_1+x_2$ , subject to $x_1+x_2\le 10,-2x_1+3x_2\le 15,x_1\le 6,x_1,x_2\ge 0$ has maximum value _________ of the feasible region.

• A

  at only one point
• B

  at only two points
• Correct answer
  C

  at every points of the segment joining two points
• D

  at every points of the line joining two points

Solution

The graph of the feasible region for the given L.P.P is

 
The value of objective function at corner points are
$z={\left[x_1+x_2\right]}_O=0$
$z={\left[x_1+x_2\right]}_E=6$
$z={\left[x_1+x_2\right]}_F=10$
$z={\left[x_1+x_2\right]}_G=10$
$z={\left[x_1+x_2\right]}_D=5$
Since the objective function is maximized at both points F and G, hence it will have a maximum value at every points of the segment joining points F and G

Hence, the correct answer is option: 'C'.