$7.$ Leo Tard owns Flex Appeal Gym a physical fitness center. Leo just signed a three$-$year lease for a high$-$tech treadmill. The lease covers everything except the treadmill$$s walking belt. Replacement walking belts can be purchased for $$400$ per belt if they are delivered with the treadmill. If Leo buys them later as he needs them, then they cost $$700$ each. If Leo buys a replacement walking belt and does not use it during the three$-$year period, Leo believes that he will be able to sell them on eBay for $$100$ per belt. The probability distribution for the number of replacement belts needed during the three$-$year period is given by the following:

# of Replacement

Belts Needed

Probability

$2\mathrm{.}3$

$3\mathrm{.}3$

$4\mathrm{.}4$

a$.$ Draw the Payoff Table and the Opportunity Loss tables.

b$.$ Find the optimal action according to Maximax, Maximin, and Maximum Likelihood.

c$.$ Find the EMV of each action.

d$.$ Find EVPI.