The maximum value of *Z* = 4*x* + 2*y* subjected to the constraints 2*x* + 3*y* ≤ 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 2*x** *+ 3*y** *≤ 18 :

The line 2*x** *+ 3*y* = 18 meets the coordinate axes at *A*(9, 0) and *B*(0, 6) respectively. By joining these points we obtain the line 2*x** *+ 3*y* = 18.

Clearly (0,0) satisfies the inequation 2*x** *+ 3*y** *≤ 18. So,the region in *xy* plane which contain the origin represents the solution set of the inequation 2*x** *+ 3*y** *≤ 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.

*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.