Question #185206

Solve the ILLP given below by graphical method :

Maximum Z = 95x1 + 100x2

Subject to the constraints

5x1 + 2x2 ≤ 20

x1 ≥ 3

x2 ≤ 5

x1 , x2 are non - negative Integers


1
Expert's answer
2021-05-07T09:56:31-0400

Z=95X1+100X2Z=95X_1+100X_2 (Maximize)


The condition given:

5X1+2X2205X_1+2X_2\leq 20

X13X_1\geq3

X25X_2\leq5


In the equation 5X1+2X2=205X_1+2X_2=20


when we put X1=0X_1=0,then X2=10X_2=10

When we put X2=0X_2=0,then X1=4X_1=4


Now when we draw a graph of the line and the given points and shade accordingly then in the feasible region we got three points

that is

A(3,0)

B(4,0)

C(3,2.5)


Now value of Z at A=

ZA=95×3+0=285Z_A=95\times3+0=285


Value of Z at B=

ZB=95×4+0=380Z_B=95\times4+0=380


Value of Z at C=

ZC=95×3+100×2.5=535Z_C=95\times3+100\times2.5=535

So the maximum value is achieved at the point C and that value is 535


So we can say that the Maximum of Z is 535 and it occurred at the point (3,2.5)


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