CASE STUDY CHALLENGE
Optimization: Fuel Efficiency Analysis
Overspeeding increases fuel consumption and decreases fuel economy as a result of tyre rolling friction and air resistance. While vehicles reach optimal fuel economy at different speeds, fuel mileage usually decreases rapidly at speeds above 80 km/h.
The relation between fuel consumption F (l/100 km) and speed V (km/h) under some constraints is given as:
$$ F = \frac{V^2}{500} – \frac{V}{4} + 14 $$
On the basis of the above information, answer the following questions:
Answer the following:
| (i) | Find F, when V = 40 km/h. | [1] |
| (ii) | Find dF/dV. | [1] |
| (iii) |
(a) Find the speed V for which fuel consumption F is minimum. — OR —
(b) Find the quantity of fuel required to travel 600 km at the speed V at which dF/dV = -0.01. |
[2] |