- A lorry is driven between London and Newcastle.
In a simple model, the cost of the journey \(\pounds C\) when the lorry is driven at a steady speed of \(v\) kilometres per hour is
$$C = \frac { 1500 } { v } + \frac { 2 v } { 11 } + 60$$
- Find, according to this model,
- the value of \(v\) that minimises the cost of the journey,
- the minimum cost of the journey.
(Solutions based entirely on graphical or numerical methods are not acceptable.)
- Prove by using \(\frac { \mathrm { d } ^ { 2 } C } { \mathrm {~d} v ^ { 2 } }\) that the cost is minimised at the speed found in (a)(i).
- State one limitation of this model.