Making Decisions Based on Decision-Tree Analysis- STATISTICS

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There are three problems associated with the Week 4 and Week 5 lecture

and readings. Points will be deducted for late submissions.

1) A potentially huge hurricane is forming in the Caribbean and there

is some chance that it might make a direct hit on Isle of Palms, South

Carolina where you are director of emergency preparedness. You have

made plans for evacuating everyone from the island but such a strategy

is obviously costly and upsetting for everyone and the evacuation

decision should not be made lightly. Discuss how you would make such

as decision. IS EMV a relevant concept in the decision? Explain. How

would you evaluate the consequences of uncertain outcomes?

2) An investor has \$10,000 to invest and several options: (1) Invest

in risk-free savings account with guaranteed 3% annual return rate;

(2) Invest in safe stick with possible rate of returns of 6, 8 or 10%;

or (3) invest in risky stock with annual return rates of 1, 9 or 17%.

The investor can place all funds in any one option or split \$10,000

into two \$5,000 investments in any two of the options. The joint

probability distributions of the possible return rates for the two

sticks is given in the provided data file below. You must create a

payoff table, use DecisionTree to identify the maximum strategy, and

perform a sensitivity analysis on the optimal decision. The data file

that you need for this case is available here .

a) Create a payoff table that specifies the investor's return in

dollars in one year for each possible year and each outcome with

respect to the stick returns.

b) Use PrecisionTree to identify the strategy that maximizes the

investor's expected earning in one year from the given investment

opportunies.

c) Perform a sensitivity analysis on the optimal decision, letting the

amount available to invest and the risk-free return rate both vary,

one at a time, plus or minus 100% from their base values and summarize

3) Pizza Kong (PK) and North Grog (NG) are competitive pizza chains.

PK believes there is a 25% chance that NG will charge \$6 per pizza, a

50% chance that NG will charge \$8 per pizza, and a 25% chance that NG

will charge \$10 per pizza. If PK charges p1 and NG charges price p2 PK

will sell 100 + 25(p2 - p1) pizzas. It costs PK \$4 to make a pizza. PK

is considering charging \$5, \$6, \$7, \$8 or \$9 per pizza. To maximize

its expected profit, what price should PK charge for a pizza?

This problem is going to be done only with Excel. You will not create

a decision tree. The problem uses a number of concepts learned during

the first three weeks.

In order to tackle this problem you are going to set up an Excel

Spreadsheet to help in making the pricing decision. As you probably

have figured out by now, we need to use formulas in every possible

case in these spreadsheets. We also need to use the Data/What-if

Analysis/Data Table function that we learned in our Spreadsheet

Modeling: An Introduction handout from weeks 1 to 3 (see content

starting on A-14).

For this problem you are given prices and probabilities in terms of

what NG will charge, so you probably should enter that data. These

data are not based on formula so you just type in the values. You also

know PK's unit cost (\$4) and price (\$5) so you should enter these

values.

The next part gets a bit tricky. You need to build an array depicting

PK's price depending on NG's price. So in one column, moving down, you

list NG's price. In the next column you need to use the demand

function (100+25(p2-p1)) to determine PK's demand. The final column

depicts PK's profit for each of NG's prices. I'll let you figure this

one out. Now develop the Expected PK Profit for this final column

using the SUMPRODUCT feature. This will give you a number that you

need to do the final step described next.

Now you need to use the What-if Analysis/Data Table function to create
a table that depicts Expected PK Profit as a Function of PK Price.
Some help for this. The table will have two columns: PK Price and Exp
Profit. The first entry in the Exp Profit column will be the cell
(pointed to) where you used the SUMPRODUCT feature (see above). The
rest of this column has to be generated using the Data Table feature.
The first entry in the PK Price column is blank. Below that cell you
will list a range of PK prices: \$5, \$6, \$7, \$8 and \$9. This is how you
set up the table and prepare to use the Data Table feature.

Once you use Data Table to populate the Exp Profit values you will be
able to pick the value that answers the question for this problem.
This should get you across the finish line.

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