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Part $1$

A manager is trying to decide whether to buy one machine or two. If only one is purchased and demand proves to be$$ excessive, the second machine can be purchased later. Some sales will be$$ lost, however, because the lead time for producing this type of machine is six months. In$$ addition, the cost per machine will be lower if both are purchased at the same time.

The probability of low demand is estimated to be

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

The$$ after$-$tax net present value of the benefits from purchasing the two machines together is

$$$$80$ comma $00080,000$

if demand is low and

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

if demand is high.

If one machine is purchased and demand is$$ low, the net present value is

$$$$110$ comma $000110,000.$

If demand is$$ high, the manager has three options. Doing nothing has a net present value of

$$$$120$ comma $000120,000$;

$$subcontracting$,$

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

and buying the second$$ machine,

$$$$130$ comma $000130,000.$

Part $2$

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