Final answer:
True, using multiple starting points while solving problems with nonlinear objective functions is essential to finding the optimal solution because of the potential for multiple local optima. An analytical approach is recommended for accuracy.
Step-by-step explanation:
When solving problems with nonlinear objective functions, it is indeed true that you must enter a variety of starting points to ensure that the answer that Solver reports is actually the optimal solution. Nonlinear optimization problems can have multiple local optima; therefore, the solution you find can depend on the starting point. Using multiple starting points increases the chance of finding the global optimum, which is the best solution over all possible solutions.
To approach such problems, it's important to identify the unknown and the known variables, express the unknown variables in terms of the known variables, and then input all the known values to find the solution. This analytical approach is generally more reliable than graphical methods, which can be more prone to error and less precise.
By practicing a variety of problems, using creativity, and applying the basics until they become almost automatic, you can enhance your problem-solving skills. It's not just about using Solver but also about understanding the principles behind the problem and how to approach it from different angles for greater flexibility and accuracy.