Part 2 A truck travelling interstate, driving at a constant speed of 110km/h, gets 7km/L efficiency and loses 0.1km/L in fuel efficiency for each km/h increase in speed. Costs include diesel ($1.49/L), truck drivers wage ($35/hour), and truck maintenance and repairs ($9.50/hour). This truck is mainly used for carrying freight between Adelaide and Sydney (1375km). Show that the cost for the Adelaide - Sydney trip is $848.93. Using differentiation, show that the optimum speed for the truck to minimise operating costs is 114km/h. Show that the model can be represented by: Explain what would happen if the truck were able to maintain a constant speed over 250km/h? Is it reasonable to assume a constant speed for such a trip? What factors affect the reasonableness of the model the most? Suppose that, for every extra freight container the truck carries, the fuel efficiency drops by 0.05km/L. Suggest what will happen to the optimum travelling speed as the load of the truck's freight increases. Find a mathematical relationship between freight size and speed for which cost is a minimum. Discuss your findings