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Part $1$

A manager is trying to decide whether to buy one machine or two. If only one machine is purchased and demand proves to be$$ excessive, the second machine can be purchased later. Some sales would be$$ lost, however, because 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

$0\mathrm{.}200\mathrm{.}20$

and that of high demand to be

$0\mathrm{.}800\mathrm{.}80.$

The$$ after$-$tax NPV of the benefits from purchasing two machines together is

$$$$90$ comma $00090,000$

if demand is low and

$$$$180$ comma $000180,000$

if demand is high.

If one machine is purchased and demand is$$ low, the NPV is

$$$$100$ comma $000100,000.$

If demand is$$ high, the manager has three$$ options: $(1)$ doing$$ nothing, which has an NPV of

$$$$100$ comma $000100,000$;

$(2)$ subcontracting, with an NPV of

$$$$140$ comma $000140,000$;

and$(3)$ buying the second$$ machine, with an NPV of

$$$$120$ comma $000120,000.$

Part $2$

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