Question

Use the graphical method to solve linear programming problem
To minimize :
Z = 2x + y
Subject to constraints : 4x + y 2 80, x+5y 2115, 3x +2y = 150, x 20 and y20 .
write the point at which maximum value of z occurs.​

Answer 1

Step-by-step explanation:

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.

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