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Question

Maximize Z = x + y, subject to constraints are x - y - 1, - x + y 0 and x, y 0.

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Solution

Our problem is to maximize Z = x + y ........(i)

Subject to constraints are x - y -1 .......(ii)

- x + y 0 ...........(iii)

x 0, y 0 ........(iv)

Firstly, draw the graph of the line x - y = -1

x01y10

Putting (0, 0) in the inequality x - y - 1, we have

00101 (which is false)

So, the half plane is away form the origin.

Secondly, draw the graph of the line - x + y = 0

x01y01

Putting (2, 0) in the inequality - x + y 0, we have - 2 + 0 2+00

20 (which is true)

So, the half plane is towards the X - axis.

Since, x, y 0

So, the feasible region lies in the first quadrant. From the above graph, it is clearly shown that there is no common region. Hence , there is no feasible region and thus Z has no maximum value.

Note If there is no common region, then we do not determine the minimum / maximum value.


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