Select a strategy using each of the following rule. | Strategy | States-of-nature $E_1$ | States-of-nature $E_2$ | | --- | --- | --- | | $S_1$ | $40$ | $60$ | | $S_2$ | $10$ | $-20$ | | $S_3$ | $-40$ | $150$ | (i) Maximin (ii) Minimax

> > [!TLDR] > Maximin selects the max of the row minima $\Rightarrow S_1$; Minimax selects the min of the row maxima $\Rightarrow S_2$. > > List the row minimum and maximum of each strategy: > > | Strategy | $E_1$ | $E_2$ | Row min | Row max | > | --- | --- | --- | --- | --- | > | $S_1$ | 40 | 60 | 40 | 60 | > | $S_2$ | 10 | $-20$ | $-20$ | 10 | > | $S_3$ | $-40$ | 150 | $-40$ | 150 | > > **(i) Maximin.** Take the maximum among the row minima $\{40,-20,-40\}$; the largest is $40$, corresponding to $S_1$. So under Maximin, select **$S_1$**. > …

Select a strategy using each of the following rule – Class 12 Business Mathematics Statistics

Question 22 of 38

Select a strategy using each of the following rule.

Strategy	States-of-nature $E_1$	States-of-nature $E_2$
$S_1$	$40$	$60$
$S_2$	$10$	$-20$
$S_3$	$-40$	$150$

(i) Maximin (ii) Minimax

Puducherry TnboardTamil Nadu HSC (DGE) Commerce Board 2022Subjective· 3mImportance★★★★★

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Maximin selects the max of the row minima $\Rightarrow S_1$ ; Minimax selects the min of the row maxima $\Rightarrow S_2$ .

List the row minimum and maximum of each strategy:

Strategy	$E_1$	$E_2$	Row min	Row max
$S_1$	40	60	40	60
$S_2$	10	$-20$	$-20$	10
$S_3$	$-40$	150	$-40$	150

(i) Maximin. Take the maximum among the row minima $\{40,-20,-40\}$ ; the largest is $40$ , corresponding to $S_1$ . So under Maximin, select $S_1$ .

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