Calculus - Differentiation: A truck travelling interstate, driving at a constant spee

[rajchris]

Hi Everyone,
I am new to the Forum and apologies if I am not following rules.
I have a difficult Math question and was wondering if anyone could help me? Details below:

Question:
A truck travelling interstate, driving at a constant speed of 110km/h, gets 7km/L efficiencyand 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).

Using differentiation, show that the optimum speed for the truck to minimiseoperating costs is 114km/h.

Show that the model can be represented as
C = 1375(801- 2.96x)
--------------------
x(18-0.1x)

Thank you. Much appreciated.

 

[tkhunny]

Well, if that is the correct function, why not find the first derivative and look for a maximum value?

 

[stapel]

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).

Using differentiation, show that the optimum speed for the truck to minimize operating costs is 114km/h.

Show that the model can be represented as

. . .\(\displaystyle C\, =\, \dfrac{1375\, (801\, -\, 2.96x)}{x\, (18\, -\, 0.1x)}\)

The "model" can be found using algebra, which you studied before you started calculus. Please reply showing your thoughts and efforts with respect to creating the modelling equation. Thank you!