DECISION TREE ASSIGNMENT

Sun and Earth

$($

S&E

$)$

$$is a company set up to

conduct geological explorations of parcels of

land in order to ascertain whether significant

metal deposits

$($

worthy of further commercial

exploitation

$)$

$$are present or not. Current

$($

S&E

$)$

has an option to purchase outright a parcel of

land for

$$

$3$

$$

$.$

If

$($

S&E

$)$

$$purchases this parcel of land then it will

conduct a geological exploration of the land. Past

experience indicates that for the type of parcel of

land under consideration geological explorations

cost approximately

$$

$1$

$$

$$and yield significant

metal deposits as follows:

ams

MBA

$-$

$2019$

manganese

$1$

$\%$

$$chance

gold

$0$

$.$

$0$

$5$

$\%$

$$chance

silver

$0$

$.$

$2$

$\%$

$$chance

Only one of these three metals is ever found

$($

if at all

$)$

$,$

i

$.$

e

$.$

$$there is no chance of finding two or more of these

metals and no chance of finding any other metal.

If manganese is found then the parcel of land can be

sold for

$$

$3$

$0$

$$

$,$

$$if gold is found then the parcel of land

can be sold for

$$

$2$

$5$

$0$

$$

$$and if silver is found the

parcel of land can be sold for

$$

$1$

$5$

$0$

$$

$.$

$($

S&E

$)$

$$can$,$ if they wish, pay

$$

$7$

$5$

$0$

$,$

$0$

$0$

$0$

$$for the right to

conduct a three

$-$

day test exploration before deciding

whether to purchase the parcel of land or not. Such

three

$-$

day test explorations can only give a

preliminary indication of whether significant metal

deposits are present or not and past experience

indicates that three

$-$

day test explorations cost

$$

$2$

$5$

$0$

$,$

$0$

$0$

$0$

$$and indicate that significant metal deposits

are present

$5$

$0$

$\%$

$$of the time.If the three

$-$

day test exploration indicates

significant metal deposits then the chances of

finding manganese, gold and silver increase to

$3$

$\%$

$,$

$2$

$\%$

$$and

$1$

$\%$

$$respectively$.$ If the three

$-$

day test

exploration fails to indicate significant metal

deposits then the chances of finding manganese,

gold and silver decrease to

$0$

$.$

$7$

$5$

$\%$

$,$

$0$

$.$

$0$

$4$

$\%$

$$and

$0$

$.$

$1$

$7$

$5$

$\%$

$$respectively$.$

What would you recommend

$($

S&E

$)$

$$should do and

why? draw decision tree