$($a$)$ In a "fixed$-$order quantity model" what is the effect of decreased lead time and decreased

variability on the reorder point and on the order quantity? Write your answer in the table below

by saying either Decreases $($D$),$ Increases $($I$),$ Stays the same $($S$),$ or$,$ No answer $-$ Insufficient

information $($NA$).$

$($b$)$ Joe is a Christmas tree vendor serving his own neighbourhood. He purchases trees for $$10$

each and sells for $$25$ each. At the end of the holiday season, the unsold trees can be salvaged

at $$3$ each. From past experience, Joe is sure about the sales probabilities which are listed

below. What is the optimal number of trees that Joe should purchase?

$($c$)$ You are in the revenue management department of the ABC airlines. Your job is to decide the

number of passengers to be overbooked on a flight from New York to Los Angeles. You know

that from past records on average $20$ passengers cancel their reservation or do not show for the

flight with a standard deviation of $15$ passengers $($normal distribution$).$ The revenue of this

flight is $$300$ per passenger and if the flight is overbooked, the passengers who are not able to

be on board will have to take the next flight and therefore the airlines will have to pay these

customers a penalty of $$450$ per passenger. Assuming that the cost of operating the flight is

sunk, by how many seats should the airlines overbook the flight? $($You can refer to the following

table for the $z$ value$)$