Question $1$

$(7$ Points$)$

Suppose KFUPM decides to open a company called Fly$-$KFUPM. A study concluded that Fly$-$KFUPM must have the shown flights per day

There is about $30$ min cleaning time and boarding time for each flight.

Fly$-$KFUPM has its base in Dammam and Riyadh $($Airplane can be parked and stay overnight in a base only$).$ The business school is preparing a feasibility study but needs to know how many planes will be required to conduct all flights mentioned above. You are working over the summer for KFUPM, and you are given the task to determine the minimum number of planes required so that the schedule is met. Using the CSP solving techniques and map coloring problem formulation, suggest the assignment of minimum number of planes required such that the schedule is met while considering all constraints.

$($Show your complete working steps on the backside of this sheet and write your final answers below$)$

$1.$ What is the minimum number of planes required to meet the schedule satisfying all constraints?

$2.$ If the planes are named as $\backslash (\backslash$mathrm$\{$P$\}1,\backslash$mathrm$\{$P$\}2,\backslash$ldots $\backslash )$ and so on$,$ provide the assignment of planes to the flights $\backslash (\backslash$mathrm$\{$F$\}1,\backslash$mathrm$\{$~F$\}2\backslash ),$ F$3,$ F$4,$ F$5$ based on your CSP solution with minimum number of planes satisfying all constraints.

a$.\backslash (\backslash$mathrm$\{$F$\}1=\backslash )$

b$.\backslash (\backslash$mathrm$\{$F$\}2=\backslash )$

c$.\backslash (\backslash$mathrm$\{$F$\}3=\backslash )$

d$.\backslash (\backslash$mathrm$\{$F$\}4=\backslash )$

e$.\backslash (\backslash$mathrm$\{$F$\}5=\backslash )$