Question

Example 6. Solve the following linear programming problem :
Minimize Z = - 60x + 30y, subject to the constraints
2x – y 2-5
3x + y23
2x – 3y = 12
x, y ZO.​

Answer 1

Step-by-step explanation:

12th

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Linear Programming

Graphical Solution of a Linear Programming Problems

Solve the following Linear ...

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Asked on December 26, 2019 by

Ambika Tewary

Solve the following Linear Programming Problems graphically:

Minimise Z=x+2y

subject to 2x+y≥3,x+2y≥6,x,y≥0.

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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.