Question

Consider the linear programming problem;

 Maximise; Z = x +y , 2x + y – 3< 0, x – 2y + 1 < 0, y < 3, x < 0, y < 0 

(i) Draw its feasible region. 

(ii) Find the corner points of the feasible region. 

(iii) Find the corner at which Z attains its maximum.

Answer 1

(I) 

(ii) In the gure the shaded region ABC is the feasible region. Here the region is bounded. The corner points are A(1, 1), B(5, 3), C(O, 3). 

(iii) Given; Z = x + y

Corner points	Value of Z
A	Z = (l)+(1) = 2
B	Z = (5)+(3) = 8
C	Z = (0)+(3) = 3

Since maximum value of Z occurs at B, the solution is Z = (5) + (3) = 8.