Course:MATH110/Archive/2010-2011/003/Notes/Optimization/Problem 11

Question

A truck has to do a 150km long trip. If it drives at a constant speed of $v$ kilometres per hour, its fuel consumption in liters of gas per hour is given by

$6+{\frac {v^{2}}{300}}$

Assuming that gas costs $1.2 per litre and that the driver is paid $25 per hour, at what constant speed will the cost of the trip be minimal? Justify your answer and sketch the graph of the total cost as a function of the choice of constant speed between $v=0$km/h and $v=200$km/h.