An engineer is working on a design problem with n parameters to be chosen, and each has 3 possible values. A highly valid descriptive model is available, and he is thinking of choosing the best design simply by using the model to evaluate the effect of every combination of design parameter values.

(a) Explain why this approach will require running the descriptive model on 3n combinations of decision-variable values.

(b) For n = 10, 15, 20, and 30, compute the time a computer would require to check all the combinations, assuming that it runs 24 hours per day, 365 days per year, and that it requires 1 second to apply the model for any particular choice of design parameters.

(c) Comment on the practical limits of this

“try all combinations” analysis strategy in the light of your results from part (b).