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Question
The maximum value of Z = 4x + 2y subjected to the constraints 2x + 3y ≤ 18, x + y ≥ 10 ; x, y ≥ 0 is
Options
36
40
20
none of these
Solution
none of these
We need to maximize the function Z = 4x + 2y
Converting the given inequations into equations, we obtain
Region represented by 2x + 3y ≤ 18 :
The line 2x + 3y = 18 meets the coordinate axes at A(9, 0) and B(0, 6) respectively. By joining these points we obtain the line 2x + 3y = 18.
Clearly (0,0) satisfies the inequation 2x + 3y ≤ 18. So,the region in xy plane which contain the origin represents the solution set of the inequation 2x + 3y ≤ 18.
Region represented by x + y ≥ 10:
The line x + y = 10 meets the coordinate axes at \[C\left( 10, 0 \right)\] and D(0, 10) respectively. By joining these points we obtain the line x + y =10.
Clearly (0,0) does not satisfies the inequation x + y ≥ 10. So,the region which does not contain the origin represents the solution set of the inequation x + y ≥ 10.
Since, every point in the first quadrant satisfies these inequations . So, the first quadrant is the region represented by the inequations x ≥ 0 and y ≥ 0.
We observe that feasible region of the given LPP does not exist.
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