1. ## Decision Tree Analysis

Can someone help me out with this question. I'm attempted to do it, but I'm not sure where I'm going right or wrong. The math is relatively easy, it's just putting things together in perspective.

T&C Inc. is a manufacturing firm that produces health care equipment. The company is owned by two
brothers, Thomas and Clinton Hunter, and has one plant. The company has experienced
significant growth in demand, and the current plant does not appear to have
sufficient capacity to meet 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
T&C 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 T&C 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 net return is$58
million. Use decision tree analysis and determine the best option for T&C Inc

Now I've already attempted the question, but I'm ot sure if my perspective is right or not in my analysis. I'll just write down what I have, and if you can answer either by using a tree diagram or just by text, either would be helpful.

Will be edited .... format didn't work.

Decision 1 = Small, Medium or Large

Small = .25 dem = 40M
.75 dem = subcontract at 44M
expand at option (40%) = 42M or option 2 = 48M

Meidum = .75 dem = Do nothing = 48M
Expand = option 1 (35%) = 44m OR OPTION 2 (65%) = 54%

.25 dem = 28M

Large = .25 dem = 10M
.75 dem = 58M

Does this look accurate to you? I have yet to do the actual math for the decisions to evaluate it , but before I do that I want to know if the decision tree looks accurate. Can anyone give me any help for this? Much appreciate, thanks.