A) Find the range of the coefficient of x3 in the objective function such that p

Question

A) Find the range of the coefficient of x3 in the objective function such that present solution remains optimal.
B) Repeat A for the coefficient of x2 in the objective function.
C) Find the range of the right side of the first constraint (inequality (1)) such that the present tableau remains feasible.

5. (15 points) The LP problenm 12515 minimize 12x 18x subject to -2x2 + 5x3 +4x2x +33 = 8 (3) x, 20, i=1,2,3 s,20 i=1,2,3 has the following optimal simplex tableau: Solution Basic x 3 · -6 -1 tie Gunetion such that the

Explanation / Answer

Range of coefficient of X3 as well for coefficient of X2 in the objective function are obtained by satisfying the conditions of optimality. Note X3 is basic variable whereas X2 is non-basic variable.

for X3 we have Max.( - (11/3)/(1/6), ..) <= deltaX3 <= Min. ( -(13/3)/-(1/6), -(1/3)/-(1/6)) ratos between Z row coefficients and X3 row coefficients, Maximum for positive and minimum for negative values in the X3 row.

-22 <= deltaX3 <= 2

for non basic X2, deltaX2 <= 13/3 Coefficient in the Z row

Similarly range of righr hand side of constraints may be obtained as follows: Here the ratios will be between the value column and column corresponding to slack of the constraint, therefore for first constraint is as follows:

-(19/3) / (5/6) <= delta-b1 <= -(1/3) / (-1/6)

-(38/5) <= delta b1 <= 2

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