Amtrack operates train routes all over the United States. They are considering a new route from Rocky Mount, NC to Washington, D$.$C$.$ All seats will be business class and they are needing to make some decisions. Their financial analyst has estimated that the cost for this route will be as follows:

Number of seats in each passenger car $50$

Average load factor $(\%$ of seats filled$)80\%$

Average passenger fare $$120$

Average variable cost per passenger $$40$

Fixed operating cost per month $$2,400,000$

$1)$ What is the break$-$even point in passengers $($BEP$)$ and revenues per month on this route $($Round CM$\%$ to the nearest $10$th of a percent $($i$.$e$.,12\mathrm{.}25\%)$ and BEP to the nearest

dollar$)?$

$2)$ What is the break$-$even point in number of passenger train cars per month $($round to the

nearest whole unit$)?$

$3)$ If Amtrack raises the average passenger fare to $$150,$ it is estimated that the average load

will decrease to $60\%.$ What will be the monthly break$-$even point in the number of

passenger cars $($round to the next whole unit, you can$$t have $40\%$ of a car$).$

$4)($Refer to original data$).$ Fuel cost is a significant variable cost to any railway. If crude

oil rises by $$12$ per barrel, it is estimated that variable cost per passenger will rise to $$50.$

What would be the new break$-$even point in passengers and in number of passenger train

cars? $($round to the next whole unit because you can$$t have just a portion of a car$).$

$5)$ Amtrack has experienced an increase in the variable cost per passenger to $$60$ and an

increase in total fixed cost to $$3,000,000.$ Amtrack has decided to raise the average fare

to $$170.$ If the tax rate is $40\%,$ how many passengers per month are needed to generate

an after$-$tax profit of $$1,000,000?($round to the nearest whole dollar and round up to the

next whole unit$).$

$6)($Use the original data$).$ Amtrack is considering offering a discounted fare of $$80,$ which

they believe would increase the average load to $90\%.$ However, only the additional seats

would be sold at the discounted fare. Additional, monthly advertising cost would be

$$125,000.$ How much pre$-$tax income would the discounted fare provide, if Amtrack has

$50$ passenger train cars per day, $30$ days per month?

$7)$ Amtrack has an opportunity to obtain a new route that would be traveled $20$ times per

month with $3$ cars. Amtrack believes it can sell seats for $$125$ on the route, but the load

factor would only be $70\%.$ This route would incur fixed costs of $$200,000$ per month for

the additional crew, additional passenger train cars, maintenance and so$,$ on$.$ Variable

cost per passenger would remain $$40.$

a$.$ Should Amtrack purchase this route? Why or Why not?

b$.$ How many passenger train cars must Amtrack operate to earn pre$-$tax income of a

minimum of $$85,000$ per month on this route $($round to a whole unit$).$

c$.$ If the load factor could be increased to $75\%,$ how many passengers train cars must

be operated to earn a pre$-$tax income of a minimum of $$85,000$ per month on this

route? $($round to a whole unit$).$

d$.$ What qualitative factors should be considered by Amtrack in making the decision

about acquiring this route.

$8)$ Amtrack currently provides box lunches for each passenger. The variable cost of each

lunch is $$5,$ while the fixed costs are $$100,000.$ Bojangles has offered to supply each

lunch for $$7.$ If Amtrack outsourced the lunches the fixed would be eliminated.

a$.$ If Amtrack transported $30,000$ passengers a month should they outsource the

lunches? Explain$-$show work

b$.$ What if they had $50,000$ passengers? Explain $-$show work