Determine the maximum value of subject to the constraints:
Given that:
It is subject to constraints
Now let us convert given inequalities into equation.
We obtain following equation
The lines that represent 2x+y=6, then further meet the other axes respectively in order to get an answer. The points are to be joined to obtain the line 2x+y=6. It is then further clarified that the equation is satisfied. Then the region that contains the origin is then represented by the set of solutions of the inequation
The region represented by
The line which is parallel to the Y-axis then meets the X-axis which comes at X=2. Hence, it is clarified that (0,0) satisfies the inequation.
After plotting the equation graphically, we get an answer:
Coming to the conclusion, when we substitute the values in Z at the corner points, we get the following answer:
Therefore, the final answer is the maximum value of Z is 42 at the point (0,6).