Question $1(25$ Points$)$

A traffic signal control is being designed for a four$-$leg intersection on a divided highway with the characteristics shown in the table below. Determine an appropriate length of the yellow and all$-$red intervals for each approach.

$\backslash$table$[[$Parameter$,$N$-$S Approaches,E$-$W Approaches$],[$Number of $12$ ft lanes on each approach,$3,2],[$Design speed, $m\frac{i}{h},50,40],[$Median width, ft$,16,12],[$Grade $(\%),0,3]]$