Find Minimize Z=3x+9y subject to

x+3y≤60 , x≤y and x,y≥0

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Solution

Minimize, Z=3x+9y

Subjected to,

x+3y<=60........(1)
x<=y................(2)
x,y=>0.............(3)
x+3y<=60

x 0 60

y 20 0

x<=y

x 0 20

y 0 20

point B is calculation by the above two equations
x=y
Then,x+3x=60
4x=60
x=15
Also,y+3y=60
y=15

Therefore B=(15,15)

Then

Corner points value of Z

A(0,20) (0×3)+(9×20)=180

B(15,15) (15×3)+(15×9)=180

C(0,0) (0×3)+(0×9)=0

Hence the function Z is minimum at C(0,0).

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