The linear program (LP) follows. MAX z = c1x1 + c2x2 + c3x3 a11x1 + a12x2 - a13x

Question

The linear program (LP) follows.

MAX z = c1x1 + c2x2 + c3x3

a11x1 + a12x2 - a13x3 b1 (1)

a21x1 + a22x2 - a23x3 = b2 (2)

a31x1 + a32x2 - a33x3 b3 (3)

x1, x2, x3 0

where x1, x2, x3 are decision variables and c1, c2, c3, a11, a12, a13, a21, a22, a23, a31, a32, a33, b1, b2, b3 are parameters of (LP).

Circle the appropriate response for each independent modification of (LP) and provide a brief explanation of your answer.

1a) Changing constraint (2) to a21x1+a22x2-a23x3 b2 is a relaxation, restriction, neither, can’t tell.

1b) Changing constraint (1) to a11x1+a12x2-a13x3 - x4 b1 (with x4 0) is a relaxation, restriction, neither, can’t tell.

1c) Changing constraint (1) to a11x1+a12x2-a13x3 + x4 = b1 (with x4 0) is a relaxation, restriction, neither, can’t tell.

Explanation / Answer

1a) is a relaxation since instead of equal to we have wide choices by greater than

1b) Neither as a variable x4 also will affect the equation

1c) Restriction as less than became equal to

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