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Which of the following statements is true concerning the optimal solution of linear program with two decision variables ?

  • A.There is only one solution to a linear program.
  • B.The optimal solution is either an extreme point or is on a line connecting extreme points.
  • C.All resources must be used up by an optimal solution.
  • D.All of the above.

Answer: B

The optimal solution of a linear program with two decision variables is either an extreme point or lies on a line segment connecting two extreme points, which happens when the objective is parallel to a binding constraint.

A linear program does not have only one solution, because there can be alternative optima. Not all resources need to be used up, since some constraints may have slack. So the 'all of the above' option is wrong as well.

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