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Question

Minimise and maximise z=5x+2y subject to the following constraints :

x2y2

3x+2y12

3x+2y3

x0, y0

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Solution

The subject of constraints is :

x2y2 ...(i)

3x+2y12 ...(ii)

3x+2y3 ...(iii)

x0, y0 ...(iv)

On solving (i), we have A(0, 1), B(2, 0)

On solving (ii), we have C(0, 6), D(4, 0)

On solving (iii), we have E(1, 0), F(1, 3)

It is observed that the feasible region OBGHJ is bounded.

Thus, we use corner point method to determine the maximum and minimum value of z, where z=5x+2y

Corner PointCorresponding value of zB(2,0)10G(72,34)19H(32,154)15J(0,32)3

Hence, zmax=19 at the point G(72,34)

and zmin=3 at the point J(0,32)


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