A farmer is deciding whether to produce a vegetable called kale that she has never produced before. From previous years’ information, it has been calculated that there is a possibility of low, moderate or high demand for kale next year, with probabilities of 0.5 (low), 0.3 (moderate) and 0.2 (high). She can dedicate an area to produce a small, medium or large quantity of kale. The net profit for different realized demands and production amounts is given in the table below: Realized Demand Profit (£ 000) Low Moderate High Production Amount Small 10 20 30 Medium 0 40 80 Large -20 40 100 a) What production amount should the farmer operate if she follows expected value, maximin, maximax and minimax regret as the decision criteria? (7 marks) The farmer is also considering the possibility of extending (or maintaining at the same level) her production of lettuce. The demand for lettuce may remain ‘moderate’ (probability 0.4) or the demand may become ‘high’ (probability 0.6). The net profits are shown in the table below: Realized Demand Profit (£ 000) Moderate High Production Amount Maintain 140 140 Extend 70 200 A marketing company offers the farmer a market research service to estimate next year’s demand for lettuce. The following table shows the probabilities of estimated demands given different realized demands. Estimated Demand Profit (£ 000) Moderate High Realized Demand Moderate 0.7 0.3 High 0.4 0.6 b) What are the probabilities of there being moderate and high realized demand, given estimates of moderate and high demand? (4 marks) c) Draw a decision tree to describe the situation and find the best course of action for the company using Expected Profit as the decision criterion (assuming no cost for the market research demand estimate). (9 marks) d) What is the maximum amount of money the farmer should pay for the demand estimate of the marketing company? (2 marks) e) What is the expected value of perfect information for the next year’s lettuce demand for the farmer?
