The corner points of the feasible region determined by x+y ≤ 8, 2x+y ≥ 8, x ≥0, y ≥ 0are A(0,8), B(4,0), and C(8,0). If the objective function Z = ax + by has its maximum value on the line segment AB, then the relation between a and b is:
8a +4 = b
a = 2b
b = 2a
8b +4 = a
a = 2b
The line segment AB has the points A(0,8) and B(4,0). The objective function Z = ax + by will have a maximum value on AB if
a/b = −change in y/change in x.
Between points A and B:Slope of AB = 0−8/4 −0 =−2
Thus, the ratio a/b = 2 implies a = 2b.