For problems 1.1-1.8. identify the following problem components:(a) decision variables;(b)...

For problems 1.1-1.8. identify the following problem components:

(a) decision variables;

(b) parameters;

(c) the objective function in words; and

(d) constraints in words.

Transportation. A state highway department is planning a new toll exit for an existing turnpike. The number of toll booths to put at the exit is in question. The department wants to keep costs low by having as few booths as possible, but if the waiting lines get too long during rush hour and other peak periods it will hurt public relations, reduce the number of people who will use the exit, and, in the worst case, back waiting vehicles onto the highway—an unacceptable and potentially hazardous situation. The highway department believes that no more than six cars—on average across the lines—should be stored in the waiting lines during rush hour, but is willing to examine other average waiting-line lengths.

From data elsewhere, it estimates the arrivals at the exit during each two-minute segment of the rush hour. It knows that it takes 17 seconds to service a car at a booth, resulting in 3.53 vehicles being processed each minute by a toll attendant. The highway department decides to develop an optimization model to analyze the problem. The goal is to assess the impact of the number of toll booths on the average length of the wailing line.