A food products company is contemplating the introduction of a revolutionary new product with new packaging to replace the existing product at same price $($S$1)$ or a moderate change in the composition of the existing product with new packaging at a small increase in price $($S$2)$ or a small change in the composition of existing except the word New with a negligible increase in price $($S$3).$ The three possible states of events are $($i$)$ high increase in sales $($N$1),($ii$)$ no change in sales $($N$2)$ and $($iii$)$ decrease in sales $($N$3).$ The marketing department of the company worked out the payoffs in terms of yearly net profits for each course of action for these events $($expected sales$).$ This is represented in the following table.

State of Nature

Courses of Action

S$1$

S$2$

S$3$

N$1$

$700,000$

$500,000$

$300,000$

N$2$

$300,000$

$450,000$

$300,000$

N$3$

$150,000$

$0$

$300,000$

Which strategy should the company choose on the basis of;

Maximin criterion

Maximax criterion

Minimax Regret criterion

Laplace criterion

QUESTION $2$

A landlord wants to decide on the type of crop to be planted in his farm. The yield largely depends on the amount and time of rainfall. He estimates the profit due to this state of nature as follows;

Rainfall

Estimated profit $($ksh$.$ Per acre$)$

Crop P

Crop Q

Crop R

Substantial

$7,000$

$2,500$

$4,000$

Moderate

$3,500$

$3,500$

$4,000$

Low

$1,000$

$4,000$

$3,000$

Based on the previous experience, he allocates the probabilities of the type of rainfall as $0\mathrm{.}2,0\mathrm{.}3$ and $0\mathrm{.}5$ for substantial, moderate and low rainfall. In order to be more confident, he approaches the met department and obtains the following forecasts for the current season.

Rainfall

Estimated probabilities

Crop P

Crop Q

Crop R

Substantial

$0\mathrm{.}7$

$0\mathrm{.}25$

$0\mathrm{.}05$

Moderate

$0\mathrm{.}3$

$0\mathrm{.}6$

$0\mathrm{.}1$

Low

$0\mathrm{.}1$

$0\mathrm{.}2$

$0\mathrm{.}7$

Determine which crop the landlord should opt for and also find out, whether it will be worthwhile to obtain the forecast, if the services are to be paid for.