Answer to Question #295862 in Statistics and Probability for Arif

Question

Your Company manufactures goods for a market in which the technology of

the products is changing rapidly. The research and development department has produced a

new product which appears to have potential for commercial exploitation. A further Rs.

60,000 is required for development testing.

The company has 100 customers and each customer might purchase, at the most , one unit of

the product. Market research suggests a selling price of Ts. 6000 for each unit with total

variable costs of manufacture and selling estimated at Rs. 2000 for each unit.

As a result of previous experience of this type of market, it has been possible to derive a

probalility distribution relating to the proportions of customers who will buy the product, as

follows:

Proportion of customers: 0.04 0.08 0.12 0.16 0.20

Probability: 0.1 0.1 0.2 0.4 0.2

Determine Expected Opportunity Losses, given no further information than that stated above

and state, whether or not, the company should develop the product.

Answer 1

Since the number of customers can be 4, 8, 12, 16 or 20, these are the possible states of nature and these should also be the potential courses of action for the company.

For each course of action – state of nature combination, the payoff element would be equal to

6000*(units sold)-2000*(units manufactured)-testing cost

Payoff matrix:

Opportunity loss matrix:

The opportunity loss or regret elements will be found corresponding to each payoff element by subtracting the payoff element from the maximum payoff corresponding to that state of nature

Opportunity loss table:

Finding expected opportunity loss for each course of action:

EOL =sum of product of opportunity loss elements and their probabilities

minimum if the company manufactures 16 units. Therefore, the company can go for developing the product and manufacture 16 units to minimise EOL.