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 ?

Puducherry TnboardTamil 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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