Solve the following Linear Programming Problem graphically: Minimise Z = x + 2y subject to 2x + y ≥ 3, x + 2y ≥ 6, x, y ≥ 0.
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To solve the given LPP graphically
1) Draw all given lines,by equating to RHS
2x+y = 3
put x= 0,y = 3
put y= 0 x = 3/2
Draw a line to meet the points (0,3) (1.5,0)
by the same way the other line
Please refer attachment for the common reason bounded by all constraints.
Now to,
Minimise Z = x + 2y
Put the coordinates of A,B,C and D
A(6,0)=> Z = (6)+2(0)=6
B(1.5,0)=> Z= (1.5)+2(0)=1.5
C(0,1)=> Z=(0)+2(1)=2
D(0,3)=> Z= (0)+2(3)=6
So,the function get Minimum at x =1.5and y = 0
Hope it helps you.
1) Draw all given lines,by equating to RHS
2x+y = 3
put x= 0,y = 3
put y= 0 x = 3/2
Draw a line to meet the points (0,3) (1.5,0)
by the same way the other line
Please refer attachment for the common reason bounded by all constraints.
Now to,
Minimise Z = x + 2y
Put the coordinates of A,B,C and D
A(6,0)=> Z = (6)+2(0)=6
B(1.5,0)=> Z= (1.5)+2(0)=1.5
C(0,1)=> Z=(0)+2(1)=2
D(0,3)=> Z= (0)+2(3)=6
So,the function get Minimum at x =1.5and y = 0
Hope it helps you.
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