Minimize ` z = 6x + 4y `, subject to
` 3x + 2y ge12, x + y ge5, 0 le x le 4, 0 le y le 4`.

Explanation

First we draw the line AB and CD whose equations are :
3x+2y=12


The feasible region is XDEAY which is shaded in the figure.
The vertices of the feasible region are A (0,6) and D (5,0).
E is the point of intersection of the lines . Now solving equation (i) and (ii) we get intersecting point E (2,3). Origin do not satisfied given condition (0,0) does not present in under lined area. Calculation of minimum value :
`{:("Corner points"," "Z=6x+4y),(AtA(0,6),Z=6xx0+4xx6=24),(AtE(2,3),Z=6xx2+4xx3=24),(At D (5,0),Z=6xx5+4xx0=30):}`
Since Z has minimum value 24 at two consecutive vertices A and E of the feasible region , Z has minimum value 24 at every point of segment AE. Hence there are infinite number of optimal solutions.