Question: A LP model may have either 1 optimal solution or more than 1 optimal solution, but it cannot have exactly 2 optimal solutions. In the

  1. A LP model may have either 1 optimal solution or more than 1 optimal solution, but it cannot have exactly 2 optimal solutions.
  2. In the solution to the Blue Ridge Hot Tubs problem, the optimal values for and turned out to be integers (whole numbers). Is this a general property of the solutions to LP problems? In other words, will the solution to an LP problem always consist of integers? Why or why not?
  3. To determine the feasible region associated with less than or equal to constraints or greater than or equal to constraints, we graphed these constraints as if they were equal to constraints. Why is this possible?
  4. Are the following objective functions for an LP model equivalent? That is, if they are both used, one at a time, to solve a problem with exactly the same constraints, will the optimal values for and be the same in both cases? Why or why not?
  5. Which of the following constraints are not linear or cannot be included as a constraint in a linear programming problem?

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