The objective function z = x 1 + x 2 , subject to x 1 + x 2 ≤ 10 , - 2 x 1 + 3 x 2 ≤ 15 , x 1 ≤ 6 , x 1 , x 2 ≥ 0 has maximum value _________ of the feasible region.

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

The value of objective function at corner points are
$z = {[x_{1} + x_{2}]}_{O} = 0$
$z = {[x_{1} + x_{2}]}_{E} = 6$
$z = {[x_{1} + x_{2}]}_{F} = 10$
$z = {[x_{1} + x_{2}]}_{G} = 10$
$z = {[x_{1} + x_{2}]}_{D} = 5$
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

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