1. Suppose you use Solver to find the optimal solution to a maximization model. Then you remember that you omitted an important constraint. After adding the constraint and running Solver again:

a. The optimal value will always remain the same

b. The optimal value can never increase

c. The optimal value can never decrease

Justify your answer.

2. Consider an optimization model with a number of resource constraints. Why is the shadow price of a resource zero when the amount used in the optimal solution is less than the amount available?

3. Why is it generally necessary to add non-negativity constraints to an optimization model? Wouldn't Solver automatically choose non-negative values for the decision variables?