(P.B
(d) Solve the following linear programming problem graphically:
Maximise Z = 7 x + 4 y
subject to the constraints :
2 x + y s 10
x + 2 y = 12
x = 0, y 20
(P.
11
biell,
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The LPP given is:
Maximize 7x+10y subject to contsraints
4x+6y≤240⇒2x+3y≤120
6x+3y≤240⇒2x+y≤80
x≥10
y≥0
Plot the graphs of 2x+3y=120,2x+y=80,x=10. The shaded portion is the feasible region of the solution.
The corner points of the feasible region are (10,0),(40,0),(30,20) and (10,
3
100
)
Examining the objective function at these values:
(x,y) Value of objective function: 7x+10y
(10,0) 70
(40,0) 280
(30,20) 410
(10,
3
100
) 403.33
From the values, we can see that 7x+10y is maximum when x=30,y=20. The maximum value is 410
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