Make up an example, as described in Problem 7, with 20 possible investments. However, do it so the ratios of NPV to cash requirement are in a very tight range, from 3 to 3.2. Then use Solver to find the optimal solution when the Solver tolerance is set to its default value of 5%, and record the solution. Next, solve again with the tolerance set to 0%. Do you get the same solution?

Try this on a few more instances of the model, where you keep tinkering with the inputs. The question is whether the tolerance matters in these types of

“close call” problems.