The research department of Hindustan Ltd., has recommended to pay marketing department to launch a shampoo of three different types. The marketing types of shampoo to be launched under the following estimated pay-offs for various level of sales. | Types of shampoo | Estimated Sales (in units) 15000 | 10000 | 5000 | | --- | --- | --- | --- | | Egg shampoo | 30 | 10 | 10 | | Clinic shampoo | 40 | 15 | 5 | | Deluxe shampoo | 55 | 20 | 3 | What will be the marketing manager's decision if (i) Maximin and (ii) Minimax Principle applied ?

> > [!TLDR] > Maximin selects Egg shampoo (best worst-case = 10); Minimax (regret) selects Deluxe shampoo (least maximum regret = 7). > > **Pay-off table (profit for sales levels 15000, 10000, 5000):** > > | Type | 15000 | 10000 | 5000 | > | --- | --- | --- | --- | > | Egg | 30 | 10 | 10 | > | Clinic | 40 | 15 | 5 | > | Deluxe | 55 | 20 | 3 | > > **(i) Maximin criterion** — for each strategy take the minimum pay-off, then choose the maximum of those minima: > > | Type | Row minimum | > | --- | --- | > | Egg | $\min(30,10,10)=10$ | > | Clinic | $\min(40,15,5)=5$ | > | Deluxe | $\min(55,20,3)=3$ | > > Maximum of the minima $=10$ → **Egg shampoo**. > > **(ii) Minimax (regret) criterion** — form the regret (opportunity-loss) table: in each column subtract every entry from the column's maximum. > - Column 15000 (max $55$): $25,\ 15,\ 0$. > - Column 10000 (max $20$): $10,\ 5,\ 0$. > - Column 5000 (max $10$): $0,\ 5,\ 7$. > …

The research department of Hindustan Ltd., has recommended to pay marketing department to launch a shampoo of

Question 34 of 38

The research department of Hindustan Ltd., has recommended to pay marketing department to launch a shampoo of three different types. The marketing types of shampoo to be launched under the following estimated pay-offs for various level of sales.

Types of shampoo	Estimated Sales (in units) 15000	10000	5000
Egg shampoo	30	10	10
Clinic shampoo	40	15	5
Deluxe shampoo	55	20	3

What will be the marketing manager's decision if

Maximin and
Minimax Principle applied ?

Tamil Nadu DgeTamil Nadu HSC (DGE) Commerce Board 2025Subjective· 3mImportance★★★★★

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Maximin selects Egg shampoo (best worst-case = 10); Minimax (regret) selects Deluxe shampoo (least maximum regret = 7).

Pay-off table (profit for sales levels 15000, 10000, 5000):

Type	15000	10000	5000
Egg	30	10	10
Clinic	40	15	5
Deluxe	55	20	3

(i) Maximin criterion — for each strategy take the minimum pay-off, then choose the maximum of those minima:

Type	Row minimum
Egg	$\min(30,10,10)=10$
Clinic	$\min(40,15,5)=5$
Deluxe	$\min(55,20,3)=3$

Maximum of the minima $=10$ → Egg shampoo.

(ii) Minimax (regret) criterion — form the regret (opportunity-loss) table: in each column subtract every entry from the column's maximum.

Column 15000 (max $55$ ): $25,\ 15,\ 0$ .
Column 10000 (max $20$ ): $10,\ 5,\ 0$ .
Column 5000 (max $10$ ): $0,\ 5,\ 7$ . …

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2026Set MARCH2 marks
$S_1$
›Reveal solutionSolution

Take the smallest pay-off in each row, then pick the row with the largest such minimum: that is $A_4$ with value $15$ .

The maximin criterion is used for decision-making under uncertainty by a cautious (pessimistic) decision-maker who guards against the worst outcome of each action.

Step 1 — Minimum pay-off (worst state) for each action:

Action $S_1$ $S_2$ $S_3$ $S_4$ Row minimum
$A_1$ 5 10 18 25 5
$A_2$ 8 7 8 23 7

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CBSE 2020Set MARCH2 marks
$E_1$
(i) Maximin
(ii) Minimax
›Reveal solutionSolution
Maximin selects the best of the row minima ( $S_1$ ); Minimax regret selects the strategy whose largest regret is smallest ( $S_3$ ).

Pay-off matrix (rupees):

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

Maximin criterion (pessimistic — best of the worst pay-offs). Take each row's minimum, then the maximum of those minima: $\max\{40,\ -20,\ -40\} = 40 \ \Rightarrow\ \textbf{Strategy } S_1.$

Minimax (regret) criterion (Savage). Build the regret (opportunity-loss) table: in each state, regret $=$ (best pay-off in that column) $-$ (pay-off). Column maxima are $E_1 = 40$ , $E_2 = 150$ .

Strategy $E_1$ regret $E_2$ regret Max regret
$S_1$ $40-40=0$ $150-60=90$ 90
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Action	$S_1$	$S_2$	$S_3$	$S_4$
$A_1$	5	10	18	25
$A_2$	8	7	8	23
$A_3$	21	18	12	21
$A_4$	30	22	19	15

Action	$S_1$	$S_2$	$S_3$	$S_4$	Row minimum
$A_1$	5	10	18	25	5
$A_2$	8	7	8	23	7

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

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

Strategy	$E_1$ regret	$E_2$ regret	Max regret
$S_1$	$40-40=0$	$150-60=90$	90

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