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Q176Section III (Statistics)176 of 180

Simplex sensitivity — re-checking optimality after a cost change

The final tableau of the simplex method of the LPP Max:Z=3x1+2x2\text{Max}:Z=3x_1+2x_2 is given below:

cj3200x1310.750.25030x4002.25−0.25060zj−cj:00.250.75090\begin{array}{c|c|cccc|c} & c_j & 3 & 2 & 0 & 0 & \\ \hline x_1 & 3 & 1 & 0.75 & 0.25 & 0 & 30\\ x_4 & 0 & 0 & 2.25 & -0.25 & 0 & 60\\ \hline z_j-c_j: & & 0 & 0.25 & 0.75 & 0 & 90 \end{array}

If the coefficient of x1x_1 in the objective function is changed from 3 to 1, then which of the following statements is/are true? (I) x2x_2 enters as a new basic variable in place of x4x_4. (II) The optimal value decreases by 33.33.

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