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Consider the following Linear programming problem $\text{(LPP)}$:

Maximize $z=x_1+x_2$

Subject to the constraints:

$x_1+2x_2 \leq 2000 \\ x_1+x_2 \leq 1500 \\ x_2 \leq 600 \\ \text{and } x_1, x_2 \geq 0$

The solution of the above $\text{LPP}$ is

1. $x_1=750, x_2= 750, z=1500$
2. $x_1=500, x_2= 1000, z=1500$
3. $x_1=1000, x_2= 500, z=1500$
4. $x_1=900, x_2= 600, z=1500$

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Graphical Method can be used.

On solving all the constraints, the peaks of the common area are:

A(0,0), B(0,600), C(1500,0), D(1000,500)

z is maximum on all the points of the constraint x1+x2<=1500 (as slope of z is same as the constraint)

Now lets try to eliminate the options

opt 1 and 2 can be eliminated as they are violating 3rd constraint

opt 4 can be eliminated as it is violating 1st constraint

Hence, opt 3 is the answer
by

1 vote