Minimise subject to the constraints:
It is given that:
It is subject to constraints
Now let us convert the given inequalities into equation
We obtain the following equation
The region which is represented by
The line in the sum meets the coordinate axes (7,0) and (0,7) respectively. If we join the lines, we will get the other line that is x + y =7. And then it is further clear that (0,0) satisfies the inequation. Then the origin represents the solution for the set of the inequation
The region represented by
The line 2x-3y+6=0 collides with the other axes to coordinate (-3,0) and (0,2) respectively. Then the lines are joined further to obtain the line 2x-3y+6=0. So, the part that contains the origin then represents the other solution set of the inequation
Looking at the graph we get,
The shaded region OBCD is the feasible region is bounded, so, minimum value will occur at a corner point of the feasible region.
Corner Points are O(0,0), B(0,2), C(3,4) and D(7,0)
Now we will substitute these values in Z at each of these corner points, we get
So, the final answer of the question is the minimum value of Z is -30 at the point of (0,2).