(a) Optimist's strategy: making repairs
(b) Pessimist's strategy: making no repairs
(c) Considering probabilities: making repairs with an expected cost of $54.
a) Optimist's Strategy:
The optimist would recommend the strategy with the maximum payoff for each state of nature.
For 0.01, the payoffs are $160 for making repairs and -$160 for making no repairs. So, the optimist would recommend making repairs.
For 0.10, the payoffs are -$75 for making repairs and -$200 for making no repairs. So, the optimist would recommend making repairs.
For 0.20, the payoffs are -$160 for making repairs and -$500 for making no repairs. So, the optimist would recommend making repairs.
Therefore, the optimist would recommend making repairs.
(b) Pessimist's Strategy:
The pessimist would recommend the strategy with the minimum payoff for each state of nature.
For 0.01, the payoffs are $160 for making repairs and -$160 for making no repairs. So, the pessimist would recommend making no repairs.
For 0.10, the payoffs are -$75 for making repairs and -$200 for making no repairs. So, the pessimist would recommend making no repairs.
For 0.20, the payoffs are -$160 for making repairs and -$500 for making no repairs. So, the pessimist would recommend making no repairs.
Therefore, the optimist would recommend making no repairs.
Considering Probabilities:
Calculate the expected cost for each strategy by multiplying the probability of each state of nature by the corresponding payoff and summing these values.
For making repairs: 0.60×160+0.30×(−75)+0.10×(−160) = $54
For making no repairs: 0.60×(−160)+0.30×(−200)+0.10×(−500) = -$188
Therefore, considering probabilities, the analyst should recommend making repairs with an expected cost of $54.
Question
An analyst must decide whether to recommend repairing a machine that is producing some defective items. He has already decided that there are three possibilities for the fraction of defective items: 0.01, 0.10, and 0.20. He may recommend two courses of action: repair the machine or make no repairs. The payoff matrix below represents the costs to the company in each case.
(a) What strategy should the analyst recommend if he is an optimist?
(b) What strategy should the analyst recommend if he is a pessimist?
(c) Suppose the analyst is able to estimate probabilities for the three states of nature, as shown in the table above. Which strategy should he recommend? Find the expected cost to the company if this strategy is chosen.
Based on the estimated probabilities, the analyst should recommend (making repairs, making no repairs) which carries an expected cost of __ dollars.
(Simplify your answer. Type an integer or a decimal.)