Topic: Transport and Differential Calculus

Overview: DLC built a corporate web site for a destination manangement company. Their specialty was shuttling guests from the convention center to various hotels and attractions in the area. Dan at DLC had built their corporate web site with some online accounting features to help manage the business across several locations. In the following year, Dan learned about a new challenge that the company faced. They had received some guest complaints at the peak of the summer season (during larger conferences). Their "direct bus route", which sent buses to/from single locations, was taking 30 minutes to return. Sometimes, people had to wait an extra 30 minutes for the bus to return. The waiting was bad, but the Florida heat was worse. To reduce wait time, a "circular bus route" was considered. In this scenario, buses would arrive at the convention center every 10 minutes, instead of every 30 minutes. Passengers would wait shorter times and enjoy the air-conditioned space of the buses. However, more gas would be spent. They needed a cost/benefit analysis to determine which method was best on any given day.

Demo: To solve the math problem, Dan suggested a simulation that used a form of differential calculus called "marginal cost". This calculation is normally used for optimizing the cost of production. However, in this case, other factors would be used in the formulas, like distance and boarding time. The company could then decide when to switch from "direct bus routes" to "circular bus routes" -- minimizing costs yet keeping guests happy and retaining their clients. On the following screen, you will be able to adjust distances and gas prices. Click the button below to begin.