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Use the graphical method to solve the following LP problem. Minimize Z=3x+2y Subject to the constraints 5x+y ≥ 10 x+y6 x+4y ≥ 12 and x,y 0.​

User SooIn Nam
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The optimal solution is (4,2).

How to minimize an objective function graphically.

Given

Objective function Z = 3x + 2y and constraints:

5x + y => 10

x + y => 6

x + 4y => 12

x => 0, y => 0

The feasible region is the area where all these constraints overlap.

Let's plot the following

Plot the line 5x + y = 10 and shade the region above this line.

Plot the line x + y = 6 and shade the region above this line.

Plot the line x + 4y = 12 and shade the region above this line.

Consider x =>0 and y =>0

The feasible region is where all shaded regions overlap.

From the graph, the possible solution points are (0,9), (4,2) , (12,0)

Let's find the value of the objective function at each point

For (0,9)

Z = 3x + 2y

= 3(0) + 2(9)

Z = 18

For (4,2)

Z = 3(4) + 2(2)

= 12 + 4 = 16

For (12, 0)

Z = 3(12) + 2(0)

= 36 + 0 = 36

The point (4,2) minimizes Z

The optimal solution is (4,2).

Use the graphical method to solve the following LP problem. Minimize Z=3x+2y Subject-example-1
User Oreopot
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