Data Analytics 19584511

An investor with $10,000 available to invest has the following

options: (1) he can invest in a risk-free savings

account with a guaranteed 3% annual rate of return;

(2) he can invest in a fairly safe stock, where the possible

annual rates of return are 6%, 8%, or 10%; or

(3) he can invest in a more risky stock, where the possible

annual rates of return are 1%, 9%, or 17%. The

investor can place all of his available funds in any one of

these options, or he can split his $10,000 into two $5000

investments in any two of these options. The joint probability

distribution of the possible return rates for the

two stocks is given in the file P06_34.xlsx.

a. Identify the strategy that maximizes the investor’s

expected one-year earnings.

b. Perform a sensitivity analysis on the optimal decision,

letting the amount available to invest and the risk-free

return both vary, one at a time, plus or minus 100%

from their base values, and summarize your findings.

35. A buyer for a large department store chain must

place orders with an athletic shoe manufacturer six

months prior to the time the shoes will be sold in

the department stores. The buyer must decide on

November 1 how many pairs of the manufacturer’s newest

model of tennis shoes to order for sale during the

coming summer season. Assume that each pair of this

new brand of tennis shoes costs the department store

chain $45 per pair. Furthermore, assume that each pair

of these shoes can then be sold to the chain’s customers

for $70 per pair. Any pairs of these shoes remaining

unsold at the end of the summer season will be sold in

a closeout sale next fall for $35 each. The probability

distribution of consumer demand for these tennis shoes

during the coming summer season has been assessed by

market research specialists and is provided in the file

P06_35.xlsx. Finally, assume that the department store

chain must purchase these tennis shoes from the manufacturer

in lots of 100 pairs.

a. Identify the strategy that maximizes the department

store chain’s expected profit earned by purchasing and

subsequently selling pairs of the new tennis shoes. Is a

decision tree really necessary? If so, what does it add

to the analysis? If not, why not?

b. Perform a sensitivity analysis on the optimal decision,

letting the three monetary inputs vary one at a time

over reasonable ranges, and summarize your findings.

Which of the inputs appears to have the largest effect

on the best solution?

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