$3-$phase signal system is to be designed for a major intersection in an urban area. The critical flow

ratios for phases $1,2$ and $3$ are $0\mathrm{.}31,0\mathrm{.}22$ and $0\mathrm{.}25,$ respectively, and the total lost time is $8\mathrm{.}0$ seconds

per cycle, determine

A$.$ the optimal cycle length, based on your calculations $($in seconds$)(5$ points$)$

B$.$ the optimal cycle length, to the next highest multiple of $5$ seconds $($in seconds$)(2$ points$)$

C$.$ based on your response to $($b$),$ the effective green time available in each cycle. $(3$ points$)$