Find the cost model in relation to the speed?

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ybyn5

Mathematics

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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 model can be represented as C= 1375 ( 801 − 2.96 x ) x (18 − 0.1x ) (C=cost x=speed) ▪ Explain what would happen if the truck were able maintain a constant speed of 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. Make a conjecture about 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. Explain how this process supports or refutes your conjecture.
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