Problem $4.$ National Budget Airlines has just been awarded a new route between $Y$ and $Z,$ and will use a leased plane to fly $2$ full circuits per day $(4$ daily flights$).$ There are other carriers on the route and the passenger demand is uncertain. You are in charge of considering three options to lease for this route. Planes will fly approximately $14$ hours per day for $365$ days per year. The annual lease cost includes all maintenaance and other consumables except fuel. Cost of jet fuel is estimated at $$\frac{6}{?}$ gallon. The annual lease$/$maintenance cost $($LMC$)$ in millions, the fuel consumption rate in gallons per hour, and the seat capacity per plane are provided next.

$\backslash$table$[[$Plane$,$LMC$/$Y$,$G$/$hr$,$Capacity$],[737,$$$26\mathrm{.}4,900,200],[787,$$$33\mathrm{.}6,1,750,270],[777,$$$32\mathrm{.}1,2,700,350]]$

Assume there are three possible demand $/$ revenue scenarios:

A$.220$ passengers$/$ flight and $$\frac{380}{?}$ passenger$-$flight.

B$.280$ passengers $/$ flight and $$\frac{480}{?}$ passenger$-$flight.

C$.320$ passengers$/$flight and $$\frac{530}{?}$ passenger$-$flight.

To do

Develop a payoff table $($in $$\frac{M}{Y}).$ Implement in Excel and have the cost of fuel as a refenced variable $($see X$-$Tree example where the cost per container is referenced from Cell D$3).$

Determine the decision for each model with no probabiltiy estimate $($optimistic$,$ conservative, min$-$max regret$).$

What is the decision if the probabilities are $A=20\%,B=45\%,C=35\%$

Create a sensitivity analysis graph for the cost of jet fuel from $$3$ to $$10.$