# Mathematical Modelling Homework

Considering a situation in which two motorists, person A and B, share the same driving route but own different sized vehicles. Person A fills up the vehicle’s tank at a station along normal route for $US"x_1"$ per litre. On the other hand, person B drives an extra $"d"$ kilometres out of his normal route to fill up his vehicle’s tank for US $"x_2"$ per litre where $x_2 < x_1$ .

1) Choose suitable parameters for Person A and B's vehicles. Justify your choices. For this question, What are the parameters?

Are the parameters the choices of the vehicle?:

1- speed - maximmumm speed and acceleration

2- Weight

3- engine output - power and torque

4- Fuel consumption - relationship between fuel and the distance

2) On a spreadsheet, choose several sets of values for $x_1$ , $x_2$ and $d$ to investigate further.

3) Define a set of variables that would be relevant in the above situation.

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Hint: Under 1), which of the parameters are useful in this calculation? The general idea is that you will use some fuel driving to the cheaper gas station. What is the tradeoff that makes it worthwhile?

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