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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