A manager is trying to decide whether to build a$$ small, medium, or large facility. Demand can be$$ low, average, or$$ high, with the estimated probabilities being $0\mathrm{.}25,0\mathrm{.}40,$ and $0\mathrm{.}35,$ respectively.

A small facility is expected to earn an$$ after$-$tax net present value of just $ $11$ comma $000$ if demand is low. If demand is$$ average, the small facility is expected to earn $ $15$ comma $000$; it can be increased to medium size to earn a net present value of $ $60$ comma $000.$ If demand is$$ high, the small facility is expected to earn $ $50$ comma $000$ and can be expanded to medium size to earn $ $90$ comma $000$ or to large size to earn $ $165$ comma $000.$

A$$ medium$-$sized facility is expected to lose an estimated $ $75$ comma $000$ if demand is low and earn $ $90$ comma $000$ if demand is average. If demand is$$ high, the$$ medium$-$sized facility is expected to earn a net present value of $ $100$ comma $000$; it can be expanded to a large size for a net payoff of $ $115$ comma $000.$

If a large facility is built and demand is$$ high, earnings are expected to be $ $180$ comma $000.$ If demand is average for the large$$ facility, the present value is expected to be $ $80$ comma $000$; if demand is$$ low, the facility is expected to lose $ $80$ comma $000.$

Part $2$

Choose the correct decision tree below. Note that each payoff is given in thousands$($$$000).$