Final answer:
Option 1 is correct. In what-if analysis for problems with two decision variables, graphical representation is indeed possible, Solver can assist with what-if reports, and shadow prices remain valid regardless of the number of decision variables.
Step-by-step explanation:
For a problem with two decision variables, we can explore the veracity of the following statements regarding what-if analysis:
What-if analysis can be done graphically. This is true, especially in problems with only two decision variables, as it allows us to visualize relationships and the impact of changing one variable on the other on a two-dimensional graph.
Solver will generate reports to assist with what-if analysis. This is true, as Solver, which is a tool in programs like Microsoft Excel, can indeed create different reports including sensitivity analysis, which is a form of what-if analysis.
Shadow prices will not be valid with only two decision variables. This statement is false. Shadow prices, which indicate how much the objective function would improve if there was one more unit of a resource, are valid no matter the number of decision variables as long as it is a constraint in a linear programming problem.
While economic models can be solved using both graphical and analytical techniques, analytical solutions are often more precise. This is because graphical methods are limited by the accuracy of the visuals and can become imprecise when dealing with very small or large values, or when a high degree of precision is required. Analytical techniques, in contrast, involve mathematical calculations that can provide a more accurate result, particularly for complex models or when precise data is crucial.