32. T F Ifall the numbers in the pivot column are negative, this implies that th
ID: 345105 • Letter: 3
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32. T F Ifall the numbers in the pivot column are negative, this implies that the 33. T F As we are doing the ratio calculations for a simplex iteration, if there is a 34. T F Shadow prices are the negative numbers in the Cj-Zj row's slack 35. T F A surplus variable is added to an" constraint in order to create an solution is unbounded. tie for the smallest ratio, the problem is degenerate. variables columns equality, and it represents a quantity of unused resource. There are no limitations on the number of constraints or variables that can be graphed to solve a linear programming problem. An objective function is necessary in a maximization problem but is not 36. TF 37. T F required in a minimization problem 38. TF When two or more constraints conflict with one another, we have a condition called unboundedness. ny time that we have an isoprofit /isocost line that is parallel to a constraint, we have the possibility of multiple solutions. The solution to a linear programming problem must always lie on a constraint 40. T FExplanation / Answer
32. If all the numbers in the pivot column is negative, this implies that the solution is unbounded. This statement is True.
Unbounded solution is the situation when the objective function value is infinite. This happens without violating any constraints in the problem.
This results in either increase or decrease in the objective function as per the minimization and maximisation problem.
The condition of detecting the unbound of the solutions are either by encountering the pivot column which does not contains the any positive entry.
33. This statement “As we doing the ratio calculation in simplex iterations, if there is a tie for the smallest ratio then the problem is degenerate.” is True.
In the simplex Method, in order to calculate the minimum coefficient or feasible condition, if there is a tie for the minimum ratio then it can be broken arbitrarily. At this particular instance at least one basic variable will become Zero. This would confirm that the solution is degenerate. This indicates that the model has at least one redundant constraint.
34. A shadow price represents the change in the objective function. This change would come from the addition or subtraction of a unit of a resource. The unit of resource may be machine time or labour time.
It is the form of sensitivity analysis. It shows that the level of sensitivity of the optimal value of the objective function would be to adding or reducing resources.
The Shadow prices are always an absolute value taken in the Cj-Zj row’s slack variable columns. It avoids the negative sign of the value.
Hence the solution is false.
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