Mege$-$Mart, a large discount store, was running a contest. The prize was a five$-$minute

shopping spree. The rules for the spree were simple. The shopping spree would take place one

week after the winner was announced, before the store opened at $9am.$ The winner would keep

all the items he or she could personally carry to the front of the store within five minutes.

However, a shopping cart or any other item with wheels could not be used to carry the items. For

example, the winner could pick up a wheelbarrow and roll it to the front of the store as a prize but

could not use it to carry other items.

Jennifer Morgan, a student, was the contest winner. She excitedly called her family, who

live in the same area, with the good news. It was great timing for Jennifer, she has recently

moved to an apartment with a friend, and there were many things that she neeci$$d but could not

afford. She eagerly made a list of the thingt she wanted: a new TV$,$ a stereo$/$ CD player, a new

computer for school, a new bike to ride to sitol, and a microwave oven. However, that evening,

as she was having dinner at her parent's houn, her older brother, Roy, mentioned that he had

been looking at a set of golf clubs at the if she got all her stuff and had a few seconds

left maybe she could pick them up for him. Hor older brother, Stewart, overhearing Roy's request,

said he could use a new chain saw. Later at dinner, her father said he would really like a riding

mower he saw at Mega$-$Mart, and her mother put in a request for a microwave oven and a TV$.$

Within the next few days, Jennifer's aunts and uncles called her with a similar requests, and even

her new roommate hinted that she could use a computer as long as Jennifer was planining to pick

one up for herself. Before long, Jennifer had a list that included two TV$\text{'}$s$,3$ stereo $/$ CD players, $2$

personal computers, $3$ bicycles, $2$ riding mowers, $4$ microwave ovens, a set of golf clubs, and $2$

chain saws. Since all the members of her family were helping her in some way to pay for her

college education and would continue to do so$,$ she really hated to turn anyone's request down.

Her five minutes, which had seemed so long a few days earlier, now seemed very short.

She explained her predicament to Roy and Stewart, and they suggested that she develop

a strategy. They took her to the Mega$-$Mart on a scouting expedition. First, they determineci that

each of the items on her list was too heavy for her to carry more than one at a time. Even at that,

it would be a struggle for her to carry a complete PC or roll a riding mower through the store.

Next, they timed how long it would take Jennifer to retrieve each item on her list. They estimated

that it would take $43$ seconds to get a TV$,32$ seconds for a stereo$/$CD player, $85$ seconds to get a

computer, $25$ seconds to get a bicycle, $3$ minutes to get a mower, $55$ seconds for a microwave

oven, $68$ seconds for a set of golf clubs, and $47$ seconds to get a chain saw. Jennifer was good in

shape $($ she swims and does aerobics$),$ so they felishe could easily go all out for the full $5$

minutes without any deterioration in effort.

A little arithmetic told them there was no way Jennifer could get all the items that had

been requested. Roy and Stewart told her she would have to make a decision on who she

wanted to make happy. Jennifer pondered that for a moment, and then came up with a decision

rule. She noted that a friend had suggested that she should simply get the most expensive items

and then sell everything. Jennifer did not went to sell but would instead maximize the total value

of the items she selected. That was a logic that she thought everyone would understand. So the

three of them went back through the store and got the retail price of each item. The price of a TV

is $$610,$ a stereo $/$ CD player is $$450,$ a PC is $$1700,$ a bike is $$360,$ a mower is $$1200,$ a

microwave oven is $$520,$ the golf clubs are $$730,$ and a chain saw is $$390.$

Now all Jennifer needed to do is use this information to develop a strategy for picking items.

Use DP to determine which items, and how many of each, Jennifer should attempt to

retrieve in the contest.

Suppose Jennifer decides at the last minute not to get multiple items but to simply get

one of everything she can. How, if at all, would this change her strategy?

Could Jennifer have used a different management science technique to solve her

problem? If so$,$ solve the problem using this other technique.

a$.$ Find EVPI for this problem.

b$.$ Does the answer in part $($a$)$ indicate that it might be worthwhile to perform this market

research?

c$.$ Develop a probability tree diagram to obtain the posterior probabilities of the two levels of

demand for each of the two possible outcomes of the market