A freeway is being designed to carry a heavy volume of $5,000ve\frac{h}{h}$ on a regular weekday in a rolling terrain. If the PHF is $0\mathrm{.}9$ and the traffic consists of $90$ percent passenger cars and $10$ percent trucks, determine the number of $12-ft$ lanes required in each direction if the highway is to operate at level of service C$.$ The free$-$flow speed is $70m\frac{i}{h},$ there is no lateral obstruction, and interchanges are $3mi$ apart.