Problem $3(30$ pts$)$

You're interning for an airline, and they're trying to determine the sequence of flights that minimizes the operating costs in a given week. Each flight must happen at least once a week. The airline has $3$ crew teams. Each crew team must be assigned to a single sequence of flights. There is a cost associated with assigning a crew team to a sequence of flights.

$\backslash$begin$\{$tabular$\}\{|$l$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline & $\backslash$multicolumn$\{11\}\{|$c$|\}\{$ Flight sequences $\}\backslash \backslash$

$\backslash$hline Flights & $\backslash (\backslash$mathbf$\{1\}\backslash )$ & $\backslash (\backslash$mathbf$\{2\}\backslash )$ & $\backslash (\backslash$mathbf$\{3\}\backslash )$ & $\backslash (\backslash$mathbf$\{4\}\backslash )$ & $\backslash (\backslash$mathbf$\{5\}\backslash )$ & $\backslash (\backslash$mathbf$\{6\}\backslash )$ & $\backslash (\backslash$mathbf$\{7\}\backslash )$ & $\backslash (\backslash$mathbf$\{8\}\backslash )$ & $\backslash (\backslash$mathbf$\{9\}\backslash )$ & $\backslash (\backslash$mathbf$\{10\}\backslash )$ & $\backslash (\backslash$mathbf$\{11\}\backslash )$ & $\backslash (\backslash$mathbf$\{12\}\backslash )\backslash \backslash$

$\backslash$hline A to B & x & & & x & & & x & & & x & & $\backslash \backslash$

$\backslash$hline A to C & & x & & & x & & & x & & & x & $\backslash \backslash$

$\backslash$hline A to D & & & x & & & x & & & x & & & x $\backslash \backslash$

$\backslash$hline B to E & & & & x & & & x & & x & x & & x $\backslash \backslash$

$\backslash$hline B to F & x & & & & & x & & & & x & x & $\backslash \backslash$

$\backslash$hline E to C & & & & x & x & & & & x & & & $\backslash \backslash$

$\backslash$hline E to D & & & & & & & x & x & & x & x & x $\backslash \backslash$

$\backslash$hline C to F & & x & & x & x & & & & x & & & $\backslash \backslash$

$\backslash$hline C to E & & & & & x & & & x & & & x & $\backslash \backslash$

$\backslash$hline F to A & x & & x & x & & x & & & & & & $\backslash \backslash$

$\backslash$hline D to F & & & x & & & & x & x & & & & x $\backslash \backslash$

$\backslash$hline D to B & & & & & & x & & & x & x & x & x $\backslash \backslash$

$\backslash$hline $\backslash$hline $\backslash$begin$\{$tabular$\}\{$l$\}$

Operating $\backslash \backslash$

Cost

$\backslash$end$\{$tabular$\}$ & $2$ & $3$ & $4$ & $6$ & $7$ & $5$ & $7$ & $8$ & $9$ & $9$ & $8$ & $9\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

a$)$ Write an integer program that determines the crew assignments to cover all the flights and minimizes the total cost $($no i$\text{'}$s$,$ j$\text{'}$s$,$ or sigmas$).$ For each constraint written, be sure to describe in words what that constraint represents. $(15$ pts$)$

b$)$ Solve the IP found in part a using Excel Solver. Provide a screenshot of the solved IP$,$ as well as of the Excel Solver window $($pre$-$solved$).(10$ pts$)$

c$)$ Which sequence of flights are assigned a crew team? $(5$ pts$)$