Question

The maximum value of Z = 4x + 2y subjected to the constraints 2x + 3y ≤ 18, x + y ≥ 10; x, y ≥ 0 is
(a) 36
(b) 40
(c) 20
(d) none of these

Answer 1

(d) none of these

We need to maximize the function Z = 4x + 2y

Converting the given inequations into equations, we obtain

$2x+3y=18,x+y=10,x=0\mathrm{and}y=0$

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.

Region represented by x ≥ 0 and y ≥ 0:
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.