Question

please use attached photo for reference to the following questions.

The local operations manager for the Internal Revenue Service must decide whether to hire one, two, or three temporary tax examiners for the upcoming tax season. She estimates that net revenues (in thousands of dollars) will vary with how well taxpayers comply with the new tax code just passed by Congress, as follows: NUMBER OF EXAMINERS One Two Three COMPLIANCE LOW NORMAL 50 50 100 60 150 70 HIGH 50 20 -10

1. using the Conservative (aka macimin) strategy: what is the net revenue (in thousands of dollars) under the worst-case scenarko for "one examiner"?

2. using the Conservative (aka maximin) strategy: what is thr net revenue (in thiusands of dollars) under the worst case scenario for "two examiners"?

3. using the Conservative (aka maximin) strategy: what is thr net revenue (in thiusands of dollars) under the worst case scenario for "three examiners"?

4. if she uses the conservative (aka maximin) strategy, how many new examiners will she decide to hire?

5. using the opportunity-loss (aka minmax regret) strategy: what is the maximum regret if "one examiner" is hired?

6. using the opportunity-loss (aka minmax regret) strategy: what is the maximum regret if "two examiners" are hired?

7. using the opportunity-loss (aka minmax regret) strategy: what is the maximum regret if "three examiners" are hired?

8. if she hses the opportunity-loss (aka minmax regret) strategy, how many new examiners will she decide to hire?

Answer 1

Sol:

For maximin

The Maximin approach is the maximum of the minimum payoffs from all the alternatives. This means we need to find the worst case for each alternative. then out of all the worst case payoffs, we need to elect the best payoffs. This is known as the conservative approach.

For the given scenario, the maximin outcome is = 50 for the one as below

	Compliance		Worst	Maximin
No. of examiners	Low	Normal	High
One	50	50	50		50	Best among all the worst payoffs is 50. Thus as per maximin criteria, we need to select the best among all the worst in each alternatives.
Two	100	60	20		20
Three	150	70	-10		-10

The Net revenue under the worst case scenario for the three examiners is -10 payoffs, for the high compliance category. Because in Three Examiners scenario, the high category got the worst case pay-off. Thus High category with (-10) as the worst case pay off Three Examiner scenario.

For minmax  

We need to prepare the regret table. The regret basically means that if we choose an option and possibly better option could have been chosen then that is our regret. For example if we choose one and the compliance is low then our regret will be 150-50 = 100

So basically it is the difference between the cell and the highest value in the column. The regret table is shown below

Original
	Low	Normal	High
One	50	50	50
Two	100	60	20
Three	150	70	-10
Regret table
	Low	Normal	High
One	100	20	0
Two	50	10	30
Three	0	0	60

The maximum regret if one examiners selected is 100. This will happen if the compliance is low.