A manager is trying to decide whether to buy one machine or two. If only one machine is purch proves to be excessive, the second machine can be purchased later Some sales would be lost the lead time for delivery of this type of machine is six months. In addition, the cost per machine will be lower if both machines are purchased at the same time. The probability of low demand is estimated to be $0\mathrm{.}30$ and that of high demand to be $0\mathrm{.}70.$ The after$-$tax NPV of the benefits from purchasing two machines together is $$90,000$ if demand is low and $$180,000$ if demand is high.

If one machine is purchased and demand is low, the NPV is $$120,000.$ If demand is high, the manager has three options: $(1)$ doing nothing, which has an NPV of $$110,000$; $(2)$ subcontracting, with an NPV of $$140,000$; and $(3)$ buying the second machine, with an NPV of $$130,000.$

a$.$ Choose the correct decision tree for this problem. Note that each payoff is given in thousands of dollars.