Question

Q.2. Solve the following Linear Programming Problem graphically:
Minimize Z=4x+2y
3x+y ≥27, x + y ≥21, x + 2y ≥30, x ≥20, y ≥20.​

Answer 1

Answer:

Answer

Given objective function is Z=x+2y

We have to minimize Z on constraints

2x+y≥3

x+2y≥6

x≥0,y≥0

After plotting the inequalities we got the feasible region as shown in the image

Now there are two corner points (0,3) and (6,0) lying on same line x+2y=6

Value at corner points are :

 Corner Points Value of Z=x+2y (0,3) 6 (minimum) (6,0) 6 (minimum)Since, feasible region is unbounded. So, 6 may or may not be minimum value.

Now to check if 6 is minimum or not, we have to draw Z<6⇒x+2y<6

Since this region doesn't have any common region with feasible region. 

So, 6 is the minimum value of Z.