Operation Research (mam) Aug. 12th

One question will help you understand everything.....

Find

Max Z = 10 X1 + 15 X2

Subject to

X1 + X2 >= 2-----------(1)

3X1 + 2X2 <= 6-------------(2)

AND X1,X2>=0

The first equation X1 + X2 >= 2 goes like this.....

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As the equation is an inequality, so it should be represented by a region not line.

So, for getting whether the region will be towards or away from origin, we will find one whether the equation is valid or not at origin that is at (0,0).

The first equation is not valid since 0>=2 is not possible, the region will be away from origin.

The second equation 3X1 + 2X2 <= 6

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The second equation will be represented by a region towards the Origin since putting (0,0) gives us 0<=6 which is possible.

Now as we are given X1,X2>=0

So, it is clear that the region should lie at first quadrant.

Now combining the two to equation we get:

Given,

Max Z = 10 X1 + 15 X2

So, Putting the values of A(0,3), B(0,2) and C(2,0) in the above equation we get....

Z(A)=45

Z(B)=30

Z(C)=20

So, Max Z= 45. Ans.