The Dollar Department Store Chain Has the Opportunity of Acquiring $\quad\quad\quad\quad\quad\quad\text{State Of The Economy}\\\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text{Over The Next 5 Years}$

The Dollar Department Store chain has the opportunity of acquiring either 3,5,or 10 leases from the bankrupt Granite Variety Store chain.Dollar estimates the profit potential of the leases depends on the state of the economy over the next five years.There are four possible states of the economy as modeled by Dollar Department Stores and its president estimates P(s₁)= .4,P(s₂)= .3,P(s₃)= .1,and P(s₄)= .2.The utility has also been estimated.Given the payoffs (in $1,000,000's)and utility values below,which decision should Dollar make? Payo ff Table $\quad\quad\quad\quad\quad\quad\text{State Of The Economy}\\\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text{Over The Next 5 Years}$
$\begin{array}{l|rrrr}Decision&s_{1} &s_{2} &s_{3} &s_{4} \\\hlined_{1}--\text { buy } 10 \text { leases } & 10 & 5 & 0 & -20 \\d_{2}--\text { buy } 5 \text { leases } & 5 & 0 & -1 & -10 \\d_{3}--\text { buy 3 leases } & 2 & 1 & 0 & -1 \\d_{4}--\text { do not buy } & 0 & 0 & 0 & 0\end{array}$ Utility Table $$\begin{array} { l r r r r r r r } \text { Payoff } ( \text { in } \$ 1,000,000 ' s ) & + 10 & + 5 & + 2 & 0 & - 1 & - 10 & - 20 \\\hline \text { Utility } & + 10 & + 5 & + 2 & 0 & - 1 & - 20 & - 50\end{array}$$