The demand for a customized knee implant continues to increase at a large orthorpedic hospital. The management is evaluating three different alternatives to meet the increasing demand: purchase of one or two 3D printers and the related software or outsourcing to a manufacturer. A consultant's report indicates a 0.20 probability that demand will be low, 0.50 probability that demand will be moderate, and 0.30 probability that demand will be high. Potential profits/losses for different demand levels are presented in the below table.

Payoff: Profit in thousands for Deman levels

Buy One 3D printer -20(LOW) 75(MODERATE) 100(HIGH)

Buy Two 3D printers -40(LOW) 65(MODERATE) 135(HIGH)

Outsource 20(LOW) 45(MODERATE) 80(HIGH)

a) Draw a complete decision tree for this problem. Clearly present the decision and event nodes, the associated probabilities, and the payoffs

b) Please explain which alternative should management choose to achieve the highest expected payoff?