Decision Tree Problem: The Westside Metal (WM) 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. Today, WM has an option to purchase outright a parcel of land for S3m. If WM 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 Slm (payable at the same time as the purchase of the land), lasts 3 years, and yield significant metal depos its as follows: manganese 1% chance gold 0.05% 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 3 years from today, if manganese is found then the parcel of land can be sold for $30m, if gold is found then the parcel of land can be sold for $250m and if silver is found the parcel of land can be sold for $150m. If no metal is found, the land loses 90% of its current value ($3m) WM can, if they wish, pay $750,000 for the right to conduct a one-year test exploration before deciding whether to purchase the parcel of land or not. Such test explorations can only give a preliminary indication of whether significant metal deposits are present or not. Data indicates that test explorations indicate significant metal deposits are present 50% of the time If test exploration indicates significant metal deposits then the chances of finding manganese, gold and silver increase to 3%, 2% and 1% respectively. If the test exploration fails to indicate significant metal deposits then the chances of finding manganese, gold and silver decrease to 0.75%, 0.04% and 0.175% respectively (If test is performed, after the exploration, prices that can be obtained in each case stay the same as before) Assume MARR is 10% What would you recommend WM should do? Draw the decision tree, make sure you pay attention to the shapes of the nodes and clearly indicate the payoff at the end of each path. Demonstrate your calculations clearly that leads to your decision. a) A company working in a related field to WM is prepared to get into a partnership with WM to pay half of all costs associated with this parcel of land in return for x% of all revenues. What is the maximum x% WM should offer? b)