You work for a small retail store. You must decide how many cases of kombucha to order. Twenty cases fit on a pallet and because of shipping costs, orders must be placed in multiples of $20.$ You can either order $20,40,60,80$ or $100$ cases. Each case costs $$15.$ If you order more than $1$ pallet, you receive a discount of $5\%$ per additional pallet ordered $(2$ pallets would be $5\%,3$ would be $10\%,$ etc$).$ The cases can be sold for $$25$ each. Any that are left unsold can be sold to a discount store for$$10.$ Your records suggest that the probability that you will sell $25$ cases is $20\%,45$ cases is $45\%,65$cases is $20\%$ and $85$ cases is $15\%.$ a$)$ Construct a payoff table to provide reflect the decisions and outcomes $(10$ marks$).$ What would be your decision based on each of the following?b$)$ Maximin $(2$ marks$)$c$)$ Maximax $(2$ marks$)$d$)$ Minimax regret $(2$ mark$)$e$)$ Expected value $(1$ mark$)$f$)$ Overall what would you do$?$ Why? $(1$ mark$)$