write an optimization model for a traffic intersection with the following data and give a code to use in LINGO:

number of vehicles crossing that signal in an hour V $=2088$

number of pedestrians crossing that signal in an hour P $=128$ cycle $=90$ seconds

effective green for vehicles Xv $=50-$lost time $=50-3=47$ seconds

effective green for pedestrians Xp $=40-$lost time $=40-5=35$ seconds

perception$-$response time $=2\mathrm{.}5$ seconds

objective function $=$ Min Z $=$ Wp $($number of pedestrians per hour$)*($delay per pedestrian$)+($number of vehicles per hour$)*($delay per vehicle$)$

delay per pedestrian Dp $=(1/2($Xv $+$ Xlost$)+$ tPRT

delay per vehicle Dv $=0\mathrm{.}5$C$\{1-($Xv$/$C$)\}2/\{1-($V$/$S$)\}$

S$=$ saturation flow rate $=2400$

G or Xv $=$ effective green time for vehicles

also consider constraints for pedestrians and vehicles and cycle time

i need objective function, decision variables, constraints, and a code for LINGO