I am going to buy a family car at the beginning of the New Year. I am going to stay in the UK for the next 4 years. I am considering the possibility of being a customer of company A which sells BMW models. Not only I can buy a car from this company but I can also trade in my car at this company and have my car serviced by the company. Company A gives a warranty that the annual maintenance costs and trade-in prices will remain the same for the next 4 years.

They are: \begin{array}{cc}\hline\text{Age of Car}&\text{Annual Maintenance}&\text{Trade-in Price at the}\\&\text{Cost}&\text{end of the period}\\\hline0&{\it\unicode{xA3}}2,000&{\it\unicode{xA3}}6,000\\1&{\it\unicode{xA3}}4,000&{\it\unicode{xA3}}5,000\\2&{\it\unicode{xA3}}6,000&{\it\unicode{xA3}}4,000\\3&{\it\unicode{xA3}}7,000&{\it\unicode{xA3}}2,000\\\hline\end{array}

To avoid maintenance costs associated with an older car, I may trade in my car and purchase a new car. My wife prefers a Rover to a BMW. Company B which sells Rover models proposes similar conditions with figures in the table below:

\begin{array}{cc}\hline\text{Age of Car}&\text{Annual Maintenance}&\text{Trade-in Price at the}\\&\text{Cost}&\text{end of the period}\\\hline0&{\it\unicode{xA3}}2,000&{\it\unicode{xA3}}8,000\\1&{\it\unicode{xA3}}3,000&{\it\unicode{xA3}}7,000\\2&{\it\unicode{xA3}}7,000&{\it\unicode{xA3}}5,000\\3&{\it\unicode{xA3}}8,000&{\it\unicode{xA3}}3,000\\\hline\end{array}

I am trying to find the minimal net cost for these 4 years which he would be using the car, here is how I went with the solution:

So this would be the cost table for the BMW and Rover respectively: \begin{align}\text{BMW}\hspace{4cm}\text{Rover}\hspace{2cm}\\\begin{array}{|c|c|}\hline c_{i,j}&1&2&3&4&5\\\hline1&&8&13&20&29\\\hline2&&&7&12&19\\\hline3&&&&6&11\\\hline4&&&&&4\\\hline5&&&&&\\\hline\end{array}\quad\begin{array}{|c|c|}\hline c_{i,j}&1&2&3&4&5\\\hline1&&10&14&23&32\\\hline2&&&8&12&30\\\hline3&&&&5&9\\\hline4&&&&&4\\\hline5&&&&&\\\hline\end{array}\end{align}

By my sketch in my notebook, I see that if we got from $1$ to $3$ with BMW and then from $3$ to $5$ with Rover, then this would minimize the cost. Is this correct?

  • 1
    $\begingroup$ Difficult decision between BMW and Rover: first world problem. $\endgroup$ Jan 7, 2020 at 13:39
  • 2
    $\begingroup$ @MarkL.Stone, well, i'm poor, so best would be for me is to optimize $\endgroup$
    – Slim Shady
    Jan 7, 2020 at 13:49
  • 2
    $\begingroup$ Isn't the purchase price a cost? I don't see it listed. $\endgroup$
    – Richard
    Jan 8, 2020 at 6:16
  • 1
    $\begingroup$ the cost is 12 000, @Luke599999 $\endgroup$
    – Slim Shady
    Jan 10, 2020 at 13:27
  • 1
    $\begingroup$ I understand (and agree) with the costs in the top row of the BMW table. I don't agree with the costs in the top row of the Rover table. Shouldn't they be 6, 10, 19, 29? I also don't understand the costs in the other rows. I think they should be the same as the top row, just shifted across by one cell each time... Please explain how you got the values - maybe I'm missing something. $\endgroup$
    – tomi
    Jan 12, 2020 at 14:13


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.