Perform what$-$if analysis to determine whether it would be worthwhile to have $5,6,$ or $7$ airplanes instead of $4.$

$2.$ Now repeat part a under the more realistic assumption that there is a minimum turnaround time of $30$ minutes on the ground for unloading and loading passengers between the arrival of a flight and the departure of the next flight by the same airplane. $($Most airlines use a considerably longer turnaround time.$)$ Does this change the number of flights that can be flown?

Rachel now is considering having each of the four airplanes carry freight instead of flying empty if it flies overnight to another city. Instead of a cost of $$5,000,$ this would result in net revenue of $$5,000.$ Adapt the spreadsheet model used in part $c$ to find the feasible combination of flights that maximizes the total profit. Does this change the number of airplanes that fly overnight to another city?

The leasing cost for each airplane is $$30,000$ per day. At the end of the day, an airplane might remain in the city where it landed on its last flight. Another option is to fly empty overnight to another city to be ready to start a flight from there the next morning. The cost of this latter option is $$5,000.$

$\backslash$table$[[$Flight Number,From,To$,$Depart,Arrive,Expected Revenue $($$$000)],[1257,$Seattle,Sen Francisco,$8$:$00AM,1000AM,37],[2576,$Seattle,Portland,$9$:$30AM,1030AM,20],[8312,$Seattle,Sen Francisco,$9$:$30AM,11$:$30AM,25],[1109,$Seattle,San Francisco,$12\mathrm{.}00PM,2$:$00PM,27],[3752,$Seattle,San Francisco,$2$:$30PM,4$:$30PM,23],[2498,$Seatte,Portland,$3$:CO PM$,4$:$00$ PM$,18],[8787,$Seattle,San Francisco,$5$:$00PM,7$:$00PM,29],[8423,$Seattle,Portland,$6$:$30$ FM$,7$:$30$ FM$,27],[7922,$Portland,Seattle,$9$:$00AM,10000AM,20],[5623,$Portland,Sen Francisco,$9$:$30AM,11$:$00AM,23],[2448,$Portland,San Francisco,$11$:$00AM,12-30PM,19],[1842,$Portland,Seattle,$12$:$00$ PM$,1$:$00$ PM$,21],[3487,$Portland,Seattle,$2$:$00PM,3$:$00PM,22],[4361,$Portiand,San Francisco,$4$:$00PM,5$:$30PM,29],[4299,$Portland,seactle,$6$:$00$ FM$,7$:$00FM,27],[1288,$San Francisco,Seattle,$8$:$00AM,10000AM,32],[3335,$San Francisco,Portland,$8$:$30$ AM$,10000AM,26],[9348,$San Francisco,Seattle,$10$:$30AM,12$:$30$ PM$,24],[7400,$San Francisco,Seattle,$12\mathrm{.}00PM,2$:$00PM,27],[7328,$San Francisco,Portland,$12\mathrm{.}00PM,1$:$30PM,24],[6386,$San Francisco,Portland,$4$:$00PM,5$:$30PM,28],[6923,$San Francisco,Seattle,$5$:$00$ PM$,7$:$00$ PM$,32]]$

The accompanying table shows the $22$ possible flights that are being considered for the coming year. The last column gives the estimated net revenue $($in thousands of dollars$)$ for each flight, given the average number of passengers anticipated for that flight.

a$.$ To simplify the analysis, assume for now that there is virtually no turnaround time between flights so the next flight can begin as soon as the current flight ends. $($If an immediate next flight is not available, the airplane would wait until the next scheduled flight from that city.$)$ Develop a network that displays some of the feasible routings of the flights. $($Hint: Include separate nodes for each half hour between $8$:$00$ AM and $7$:$30$ PM in each city.$)$ Then develop and apply the corresponding spreadsheet model that finds the feasible combination of flights that maximizes the total profit.

$.$ Rachel is considering leasing additional airplanes to achieve economies of scale. The leasing cost of each one again would be $$30,000$ per day.