2 (30 marks) A vendor of ice cream buckets at the Selangor Cricket Ground has determined that sales at one day cricket matches are a function of the maximum daily temperature: Unit Sales Maximum Temperature [Celsius] 1000 Above 35 800 30 - 34 600 25 - 29 400 20 - 24 200 Below 20 The ice creams sell for $4.00 each and cost $2.00. Unsold ice creams will be worthless because the vendor has no way of storing them until the next match. Required: (a) If the vendor were a pessimist how many ice creams would he order? (b) If the vendor were an optimist how many ice creams would he order? (c) If the vendor followed the criterion of regret how many ice creams would he order? (d) Using the Laplace criterion how many ice creams would he order? (e) Based on meteorological information the vendor estimates the following probability distribution for temperature at a coming match: Temperature Probability Above 35 0.2 30 - 34 0.2 25 - 29 0.3 20 - 24 0.2 Below 20 0.1 If the vendor based his decision on maximum expected value how many ice creams would he order? (6 marks for each part)