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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 0.30 and that of high demand to be 0.70. 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 $100,000; (2) subcontracting, with an NPV of $150,000; and (3) buying the second machine, with an NPV of $120,000. a. Choose the correct decision tree for this problem. Note that each payoff is given in thousands of dollars. Buy 1 100 150 Low demand 90 Do nothing 2 machine High demand Subcontract 1 Low demand, Buy 2 120machines 3 machines High demand, 180 Buy 2 120 Buy 2 100 150 machines 1 Low demand 120Do nothing 0.70 High demand Subcontract 0.30 Buy 2 Low demand 90 machines 0.70 180 0.30 120 Buy 1 High demand 80 machine Buy 1 100 machine 1 150 Low demand, 120Do nothing 0.30 High demand Subcontract 0.70 Low demand Buy 2 90 machines 0.30 High demand 180 0.70 120 Buy 2 machines Buy 1 machine 1 Buy 2 machines Low demand, 120 0.30 Do nothing 100 High demand Subcontract 150 0.70 Buy 2 120 Low demand machines 90 0.30