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CMA Intermediate · Operations Management and Strategic Management · Optimum Allocation of Resources - LPP

In a simplex iteration, x1 is the entering variable. Its column coefficients in three constraint rows are 4, 5 and −3, with corresponding RHS values 24, 20 and 9. Which row's basic variable leaves the basis?

The basic variable in row 2 leaves the basis. The minimum ratio test uses only positive coefficients in the entering column: 24/4 = 6 and 20/5 = 4. The row with a negative coefficient is ignored, and the smallest ratio, 4, identifies row 2.

  1. ARow 2, with ratio 4Correct
  2. BRow 1, with ratio 6
  3. CRow 3, with ratio −3
  4. DRow 3, because its RHS is the smallest

Explanation

The minimum ratio test divides RHS by positive entering-column coefficients only. Row 1 gives 24/4 = 6 and row 2 gives 20/5 = 4. Row 3 has a negative coefficient and is ignored. The smallest ratio is 4, so the row 2 basic variable leaves. Picking row 3 because of its small RHS ignores the rule.

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