7. On a journey, the average speed of a car is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\). For \(v \geq 5\), the cost per kilometre, \(C\) pence, of the journey is modelled by \(C = \frac { 160 } { v } + \frac { v ^ { 2 } } { 100 }\).
Using this model,

1. show, by calculus, that there is a value of \(v\) for which \(C\) has a stationary value, and find this value of \(v\).
2. Justify that this value of \(v\) gives a minimum value of \(C\).
3. Find the minimum value of \(C\) and hence find the minimum cost of a 250 km car journey.