QUESTION $1.$

Glencore has some funds to invest in developing a new coal mine. However, due to recent events it can only afford to make one investment. The choices and pay$-$offs depend on the size of the coal find and are described in Table $1.$

Australia Chile India

Probability

Quantity of coal found Low Med High $8011013020100150$

$150502000\mathrm{.}40\mathrm{.}10\mathrm{.}5$

Table $1.$ Payoff table for Glencore$$s investment decision

$1$a$)$ Identify which decision would be taken with each of the $$decision making under uncertainty$$ criteria:

$$ Maximax;

$$ Maximin;

$$ Laplace;

$$ Minimax; Hurwitz $($with $\backslash$alpha $=0\mathrm{.}6)$; $$ and Maximum Likelihood.