Question $1$: Construction Company

A construction company must decide on the size of the shopping mall, i$.$e$.$ Large, Medium or Small, that has to be constructed in their acquired plot in the sub$-$urban area of Chicago. Due to the market conditions, the number of visitors to the mall will be High, Moderate, or Low. The level of response and the size of the mall will decide the return on investment from the mall. The profit payoff table for management $($in millions of dollars$)$ after $5$ years is provided below.

Number of visitors

Size of the mall

High

Moderate

Low

Large

$25$

$15$

$20$

Medium

$20$

$12$

$10$

Small

$15$

$13$

$5$

The probabilities for the state of nature are P$($High$)=0\mathrm{.}35,$ P$($Moderate$)=0\mathrm{.}40,$ and P$($Low$)=0\mathrm{.}25.$

A test market study of the potential response for the mall in that area is expected to report either a favorable $($F$)$ or unfavorable $($U$)$ condition. The relevant conditional probabilities are as follows:

P$($F$|$High$)=0\mathrm{.}4$; P$($U$|$High$)=0\mathrm{.}6$

P$($F$|$Moderate$)=0\mathrm{.}6$; P$($U$|$Moderate$)=0\mathrm{.}4$

P$($F$|$Low$)=0\mathrm{.}20$; P$($U$|$Low$)=0\mathrm{.}80$

Determine the decision strategy the construction company should follow $($using the expected value criterion$)$ and the expected value of this strategy.

What is the efficiency of the information provided by the test market study?