Consider the problem min zx12x2 subject to the condition tha

Consider the problem min z=x_1-2x_2 subject to the condition that two of the following three constraints must hold 2x_1 + x_2 4

First finding the intersection point of first and second line

2x1 + x2 = 4

x1 + x2 = 3

x1 = 1 and x2 = 2

Finding the intersection point of 2 and 3rd line

x2 = 5/3 and x1 = 4/3

Finding the intersection of point 1st and 3rd line

x2 = 12/7 and x1 = 8/7

Minimum value of Z at all these points

Z(1,2) = -1 -2(2) = -5

Z(5/3,4/3) = -5/3 -2(4/3) = -13/3

Z(12/7,8/7) = -12/7 - 16/7 = -4

The first and third point will not satisfy all the three criterias, hence the minium answer will be -13/3 at point (5/3,4/3)