Example 16.2 Given the following payoff function for each alternative a l and a 2
Q a1 ¼ À25 þ 40 x
Q a2 ¼ À80 þ 29 x
(i) find the break even value of x.
(ii) If x ¼ 5, which is the better alternative?
(iii) If x ¼ 5, what is the regret of the poor strategy?
(iv) If x ¼ À 10, which is the better alternative?
(v) If x ¼ À 10, what is the regret of the poor strategy?
Solution
(i) For break even point, Q a1 ¼ Q a2
À25 þ 40x ¼ À80 þ 29 x
Or 11x ¼ À55 or x ¼ À5:
Therefore, À5 is the break even point.
(ii) When x ¼ 5, Q a1 ¼ À 25 + 200 ¼ 175
Q a2 ¼ À80 þ 145 ¼ 65:
Therefore a l is the better alternative.
(iii) For x ¼ 5, the regret of the poor strategy a 2 ¼ 175À65 ¼ 110.
(iv) When x ¼ À 10, Q a1 ¼ À 25 À 400 ¼ À 425,
Q a2 ¼ À80 À 290 ¼ À370
Therefore a 2 is the better alternative
(v) For x ¼ À 10, the regret of the poor strategy a l ¼ À 370 + 425 ¼ 55.
16.6 Decision Making Under Conditions of Risk
Most business decisions are usually made under conditions of risk. Here, there are
several states of nature, and the decision maker possesses enough information to
allocate probabilities to each of these events. These probabilities are often available
or determined from past records or sometimes the decision maker can make a
16.6 Decision Making Under Conditions of Risk
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