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

In a maximisation simplex table, a variable has a positive Cj − Zj, but every coefficient in its column in the constraint rows is zero or negative. What does this indicate?

It indicates an unbounded solution. A positive Cj − Zj means the objective can still improve by increasing that variable, but with no positive column coefficients the ratio test imposes no limit. The variable can grow indefinitely, so the objective has no finite maximum.

  1. AThe problem has an unbounded solutionCorrect
  2. BThe problem has multiple optimal solutions
  3. CThe problem is infeasible
  4. DThe current solution is degenerate and optimal

Explanation

A positive Cj − Zj means increasing the variable raises the objective. If no row has a positive coefficient, the minimum ratio test has no limit, so the variable can increase indefinitely without violating any constraint. This signals an unbounded solution. Multiple optima would show a zero Cj − Zj for a non-basic variable at optimality instead.

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