MATH 1010
Introduction
This project neatly demonstrates the concept of a cost-benefit analysis, an essential practice in investment strategy. The benefits over time of a hybrid car in the form of lower gasoline consumption is weighed against the cost, the higher initial investment in the vehicle’s price. This is then compared to the same analysis performed on a conventional equivalent vehicle.
Given 1. The MSRP of each vehicle, 2. The expected rate of miles per gallon fuel of each vehicle, 3. A fixed cost of fuel, and 4. A fixed rate of mileage per month, we can derive a total cost over time for each vehicle under expected usage. The graphed lines of these costs over time intersect at just over 52 ½ months, meaning that the cost of owning and using these vehicles are equal at the point when that time has elapsed. After this point, the hybrid vehicle (theoretically) becomes a better monetary investment.
The project, given that it is a math project, is also a demonstration of the usage of several mathematic techniques. These include the use of systems of equations, solving those systems of equations via the substitution or the elimination method, the plotting of charts, and the translation of data sets into mathematical equations. By using these techniques, I was able to produce readable data with real-world implications.
Reflection
A cost-benefit analysis is useful for anyone making an investment of any significance. In this case, being a choice of vehicle purchase, most people in the United States would do well to perform this sort of analysis. Making this exact analysis, though the mathematical portion leaves out information relevant to my final conclusion and recommendation, plays an important role in deciding a course of action regarding an investment in a vehicle. Hybrids are increasingly prevalent on the market, and figuring out the actual advantages or disadvantages of the technology as compared to equivalent conventional versions is very valuable. A similar analysis could be performed on any investment with a continued cost of operation, up to and including the purchase of a business.
The scenario specified by this project’s prompt is that of a proposal to a business manager regarding procurement of fleet vehicles. Were I to play the role of the manager, I believe I would find myself satisfied by the analysis provided here. By clearly laying out the methodology and assumptions made in the process of the analysis, nothing is left as mystery. Few things are more frustrating than reading some piece of essential information without justification or support given. A conclusion without proper support calls for further analysis, requiring additional valuable time and resources to correct a flawed initial exploration. Showing how a conclusion was reached is essential, as the audience may not have implicit trust in a conclusion without provided evidence. Even if I as a business owner trust the source of this analysis implicitly, having access to the raw equations involved with the analysis would allow me to adjust the projections to suit new information such as rising gas prices or even different vehicles.
The usage of math is indispensable in cases like these. Although this fact was known to me at the outset of this project, I did find it useful to conduct this analysis and further prove, if only to myself, that I am capable of conducting a useful cost-benefit analysis with the skills I possess. Hybrid vehicles are very attractive, especially to those concerned with the effects of climate change. They are more fuel efficient, which might lead one to believe that the lower fuel cost will outweigh a higher initial price within a reasonable amount of time. However, certain disadvantages are inherent to the usage of batteries which do not apply in the same way to conventional engines. By using math to find the point at which the costs of fuel will outweigh that initial cost, we can estimate when in time that point will come in a sober and objective manner. This timeline may support the decision to buy a hybrid, or it may indicate that a conventional vehicle is a better investment. Either way, the decision can be made without interference from emotional influences so prevalent in advertising.