Problem 2 A manager must decide how many machines of a certain type to buy. The machines will be used to manufacture a new gear for which there is increased demand. The manager has narrowed the decision to two alternatives: buy one machine or buy two. If only one machine is purchased and demand is more than it can handle, a second machine can be purchased at a later time. However, the cost per machine would be lower if the two machines were purchased at the same time. The estimated probability of low demand is 0.30, and the estimated probability of high demand is 0.70. The net present value associated with the purchase of two machines initially is $75,000 if demand is low and $130,000 if demand is high. The net present value for one machine and low demand is $90,000. If demand is high, there are three options. One option is to do nothing, which would have a net present value of $90,000. A second option is to subcontract; that would have a net present value of $110,000. The third option is to purchase a second machine. This option would have a net present value of $100,000. a. Construct a decision tree for this case. b. What is the expected net present value for buying one machine initially? c. What is the expected net present value for buying two machines initially? d. How many machines should the manager purchase initially? Why?