Question $6.$

The Oahu Trading Company is considering the purchase of a small firm that produces clocks. Oahu's

management feels there is a $50-50$ chance, if Oahu buys the firm, that it can mold the firm into an

effective producer of washing machine parts. If the firm can be transformed in this way, Oahu

believes that it will make $$695,000$ if it buys the firm; if it cannot be transformed in this way,

Oahu believes that it will lose $$580,000$ if it buys the firm. The outcome is $$0$ if Oahu does not buy

the firm.

a$.$ Construct a decision tree to represent Oahu's problem. $[3$ marks$]$

b$.$ What are the decision forks? $($Are there more than one?$)[1$ mark$]$

c$.$ What are the chance forks? $($Are there more than one?$)[1$ mark$]$

d$.$ Use the decision tree to solve Oahu's problem. In other words, assuming that the firm wants to

maximize the expected profit, should Oahu buy the firm? Show your calculations. $[3$ marks$]$

e$.$ Before Oahu makes a decision concerning the purchase of the firm, Oahu's president learns

that if the clock producer cannot be made into an effective producer of washing machine parts, there

is a $0\mathrm{.}41$ probability that it can be resold to a Saudi Arabian syndicate at a profit of $$220,000.($If the

firm cannot be resold, Oahu will lose $$580,000.)$

$(1)$ How does this information alter the decision tree? Construct the new decision tree including

all outcomes. $[4$ marks$]$

$(2)$ What is the probability of each of the outcomes? $[3$ marks$]$

f$.$ Use your results in part $($e$)$ to solve Oahu's problem under this new set of conditions. In other

words, on the basis of this new information, should Oahu buy the firm? Show your calculations. $[3$

marks$]$

g$.$ If you were to alter the amount $$695,000$ so that the purchase decision of Oahu will be

reversed:

$(1)$ What would be the largest amount to replace $$695,000$ under the circumstances in part $($d$)?$

Show your calculations. $[4$ marks$]$

$(2)$ What would be the largest amount to replace $$695,000$ under the circumstances in part $($e$)?$

Show your calculations. $[4$ marks$]$