- A food product company is contemplating the introduction of revolutionary new product to replace the existing product, moderate change in design with a small increase in price or a small change in design with a negligible increase in price. The three possible states of nature are: (1) high increase in sales, (2) no change in sales and (3) decrease in sales. The profit is given in the following table: Course of action State of nature New Moderate Small (Rs.) product change in change in (N1) design (N2) design (N3) High Increase in 700,000 300,000 150,000 sales (S1) No change in sales(S2) 500,000 450,000 0 Decrease in sales (S3) -300,000 -200,000 - 100,000 Which strategy should the company choose on the basis of the following: 1) Maximin and maximax criterion (3 marks) (ii) Equally likely decision (Laplace criterion) (3 marks) (iii) Develop an opportunity loss table and hence determine the minimax regret criterion (4 marks) (b) A company is deciding whether to develop and launch a new product. Research and development costs are expected to be $400,000 and there is a 70% chance that the product launch will be successful, and a 30% chance that it will fail. If it is successful, the levels of expected profits and the probability of each occurring have been estimated as follows, depending on whether the product's popularity is high, medium or low: Probability Profits High: 0.2 $500,000 per annum for two years Medium: 0.5 $400,000 per annum for two years Low: 0.3 $300,000 per annum for two years If it is a failure, there is a 0.6 probability that the research and development work can be sold for $50,000 and a 0.4 probability that it will be worth nothing. (1) Draw a decision tree for the problem (ii) What decision should the company make based on the given information? (10 marks) - A food product company is contemplating the introduction of revolutionary new product to replace the existing product, moderate change in design with a small increase in price or a small change in design with a negligible increase in price. The three possible states of nature are: (1) high increase in sales, (2) no change in sales and (3) decrease in sales. The profit is given in the following table: Course of action State of nature New Moderate Small (Rs.) product change in change in (N1) design (N2) design (N3) High Increase in 700,000 300,000 150,000 sales (S1) No change in sales(S2) 500,000 450,000 0 Decrease in sales (S3) -300,000 -200,000 - 100,000 Which strategy should the company choose on the basis of the following: 1) Maximin and maximax criterion (3 marks) (ii) Equally likely decision (Laplace criterion) (3 marks) (iii) Develop an opportunity loss table and hence determine the minimax regret criterion (4 marks) (b) A company is deciding whether to develop and launch a new product. Research and development costs are expected to be $400,000 and there is a 70% chance that the product launch will be successful, and a 30% chance that it will fail. If it is successful, the levels of expected profits and the probability of each occurring have been estimated as follows, depending on whether the product's popularity is high, medium or low: Probability Profits High: 0.2 $500,000 per annum for two years Medium: 0.5 $400,000 per annum for two years Low: 0.3 $300,000 per annum for two years If it is a failure, there is a 0.6 probability that the research and development work can be sold for $50,000 and a 0.4 probability that it will be worth nothing. (1) Draw a decision tree for the problem (ii) What decision should the company make based on the given information? (10 marks)