Jo$-$Jo Inc. is a manufacturing firm that produces soap. The company is owned by two brothers, Donald and David Schroeder, and has one plant. The company has experienced significant growth in demand, and the current plant does not appear to have sufficient capacity to meed demand. The company has decided to build a new plant to meet the additional capacity. However, the brothers must decide whether to construct a small, medium, or large plant. The brothers hired a forecasting consultant to predict demand. The consultant's report indicates that there is a $25$ percent chance that the demand will be low and a $75$ percent chance that the demand will be high. If Jo$-$Jo Inc. builds a small facility and the demand indeed turns out to be low, the consultant expects net profit of $$40$ million. If the firm builds a small plant and the demand turns out to be high, then the firm has two options: $(1)$ subcontract or $(2)$ expand the facility. If Jo$-$Jo Inc. decides to subcontract, the expected net return will be $$44$ million. If the firm expands the new facility, there is a $40$ percent chance that the net return will be $$42$ million and a $60$ percent chance that the net return will be $$48$ million. If the medium$-$size facility is constructed and the demand turns out to be low, the net return is estimated at $$28$ million. However, if the medium$-$size facility is built and the demand turns out to be high, Jo$-$Jo inc. has two options: $(1)$ do nothing, for an expected net return of $$48$ million, or $(2)$ expand. If the firm decides to expand, there is a $35$ percent chance that it will earn a net return of $$44$ million and a $65$ percent chance that it will earn a net return of $$54$ million. If the firm decides to build a large facility and demand turns out to be low, the net return will be $$10$ million. However, if the firm decides to build a large plant and the demand turns out to be high, the expected return is $$58$ million.

Make a decision tree analysis and determine the best option for Jo$-$Jo Inc.