Rusto Farms sells produce to local markets. Management is trying to decide whether they should expand, keep the same size farm or reduce the size of the farm. They assessed the demand levels for their produce in the local market and probabilities associated with each demand level: high $($probability $0\mathrm{.}30),$ medium $($probability $0\mathrm{.}47),$ or low $($probability $0\mathrm{.}23).$ The payoffs they expect for each demand$/$acreage scenario are listed below.

Acreage

Demand Expand Same Size Contract

High $$118,000$ $$46,000$ $$26,000$

Medium $$47,000$ $$39,000$ $$26,000$

Low $$-15,700$ $$19,000$ $$26,000$

a$.$ What is perfect information about the demand worth under these circumstances? Please show your calculations. $(4$ marks$)$

b$.$ The farm has hired a consultant to forecast the demand. The consultant has predicted high demand. The accuracy of his predictions are as follows:

P$($PH $\backslash$ H$)=0\mathrm{.}71$ P$($PH$\backslash$ M$)=0\mathrm{.}20$ P$($PH $\backslash$ L$)=0\mathrm{.}09$ P$($PM $\backslash$ H$)=0\mathrm{.}17$ P$($PM $\backslash$ M$)=0\mathrm{.}70$ P$($PM $\backslash$ L$)=0\mathrm{.}19$ P$($PL $\backslash$ H$)=0\mathrm{.}12$ P$($PL $\backslash$ M$)=0\mathrm{.}10$ P$($PL $\backslash$ L$)=0\mathrm{.}72$

Where:

H $=$ high demand PH $=$ predict high demand

M $=$ medium demand PM $=$ predict medium demand

L $=$ low demand PL $=$ predict low demand

Based on the accuracy of the prediction, calculate the revised probability for each state of nature $($to $3$ decimal places$)$ given that the consultant forecast high demand. $(3$ marks$)$Question $1(7$ marks$)$

Rusto Farms sells produce to local markets. Management is trying to decide whether they should

expand, keep the same size farm or reduce the size of the farm. They assessed the demand levels

for their produce in the local market and probabilities associated with each demand level: high

$($probability $0\mathrm{.}30),$ medium $($probability $0\mathrm{.}47),$ or low $($probability $0\mathrm{.}23).$ The pay offs they expect

for each demand$/$acreage scenario are listed below.

a$.$ What is perfect information about the demand worth under these circumstances?

Please show your calculations. $(4$ marks$)$

b$.$ The farm has hired a consultant to forecast the demand. The consultant has predicted

high demand. The accuracy of his predictions are as follows:

Where:

Based on the accuracy of the prediction, calculate the revised probability for each state of nature

$($to $3$ decimal places$)$ given that the consultant forecast high demand. $(3$ marks$)$