At a decision point in a decision tree, which machine would you select when trying to maximize payoff when the anticipated benefit of selecting machine A is $45,000, with a probability of 90%; the expected benefit of selecting machine B is $80,000, with a probability of 50%; and the expected benefit of selecting machine C is $60,000, with a probability of 75%?

machine C

Explanation:

A decision tree shows the possible outcomes from making different decisions based on cost, probability and profit. Expected benefit is the product of value of an outcome and the probability.

The different machines expected benefits are:

Expected benefit for machine A = $45000 × 90% =  $45000 × 0.9 = $40500

Expected benefit for machine B = $80000 × 50% =  $80000 × 0.5 = $40000

Expected benefit for machine C = $60000 × 75% =  $60000 × 0.75 = $45000

Since machine C has the expected benefit, it be selected so as to maximize payoff

borrow money from the government then pay the government back 5k

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