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Answer :
Final answer:
Excel's Solver shows the objective function's value in the target cell after optimization and will indicate whether it found an optimal solution or not. It iterates over variable combinations within constraints until improvements are minuscule, guided by a user-set convergence criterion.
Explanation:
After running a problem through Excel's Solver, the program will display the value of the objective function in the target cell. If the Solver finds a solution, it will present the optimal values for the objective and adjustable cells, and a message window will confirm the successful operation. However, if it cannot find a feasible solution, it will still display the best values it could find but will indicate the inability to find a proper solution. Furthermore, Solver's algorithm, while naive, tries different combinations of variables and evaluates the improvement until it no longer improves substantially, influenced by the convergence criterion that users can set. This is visualized graphically in action, as demonstrated in hypothetical stylized graphs, like Figure 3.8.
Specifically, in the context of a firm's cost function and profit maximization, Excel's Solver can determine the optimal output and profit by altering input variables within defined constraints to achieve the highest profit possible. This can be especially useful when considering changes in external factors such as resource availability, technological advancements, or natural disasters affecting resources.
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