Question

9. Solve the ILLP given below by graphical method: (10)

Maximum 95 1 100 2 Z = x + x

Subject to the Constraints

5x1 + 2x2 ≤ 20

x1 ≥ 3

5 x2 ≤

1 2

x x are non-negative integers.

Answer 1

Solution:

Maximize $Z=95x_1+100x_2$

subject to the constraints:

$5x_1+2x_2≤ 20 ...(i) \\x_1 ≥ 3...(ii) \\x_2 ≤ 5...(iii)$

$x_1 , x_2\ge0$

Consider (i), (ii), (iii) equations and plotting their graph, we get,

Clearly, corner points are $(3,0),(4,0),(3,2.5)$.

At $(3,0),Z=95(3)+100(0)=285$

At $(4,0),Z=95(4)+100(0)=380$

At $(3,2.5),Z=95(3)+100(2.5)=535$

Hence, maximum value is 535 at $(3,2.5)$.