The feasible region for a LPP is shown in Fig. 12.9. Find the minimum value of
The following is given that:
It is subject to constraints
Now let us convert the given inequalities into equation
We obtain the following equation
The region represented by x + y ≤ 5:
The line that shows , then meets the axes that coordinate (5,0) and (0,5) respectively. We need to join the points in order to obtain the line . Hence, it is clarified that (0,0) then satisfies the inequation . Therefore, the region that has the origin represents the solution set of .
The region that is represented by
The line that is meets the coordinate axes (9,0) and (0,3) respectively to get the final answer. When we join the points we get the line . Therefore, it is then clear that the region doesn’t contain the origin and represents the solution set of the inequation.
The graph is further given below:
The shaded region BEC is the feasible region is bounded, so, minimum value will occur at a corner point of the feasible region.
Corner Points are B(0,3), E(0,5) and C(3,2)
Now we will substitute these values in Z at each of these corner points, we get
Hence, the minimum value of Z is 21 at the point (0,3)