Problem $3.$

Racquet Centers, Inc. $($RCI$)$ is a small investment company. The company is considering building a new racquet center. If the demand for the center is high $($i$.$e$.,$ there is a favorable market for the racquet center$),$ RCI could realize a net profit of $$100,000.$ If the market is not favorable, RCI could lose $$40,000.$ Of course, they don't have to proceed at all; in which case, there is no cost$.$ In the absence of any market data, the best RCI can guess is that there is a $50-50$ chance the center will be successful. What should RCI do$?$

Obviously they should construct the center as the following table shows the Expected Monetary value of construction the center is $$30,000.$ Probabilities

$\backslash$table$[[,$Favorable Market,Unfavorable Market,,$],[$Construct The Center,$$100,000\mathrm{.}00,($$$40,000\mathrm{.}00),$EMV $=,$$$30,000\mathrm{.}00$