Question

(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,​

Answer 1

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

Answer 2

Answer:

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