(1) An entertainment company is organizing a pop concert in London. The company has to decide how much it should spend on publicizing the event and three options have been identified.

Option 1: Advertise only in the music press.

Option 2: As option 1 but also advertise in the national press.

Option 3: As options 1 and 2 but also advertise on commercial radio.

For simplicity, the demand for tickets is categorized as low, medium or high. The payoff table below shows how the profit which the company will earn for each option depends on the level of demand.

It is estimated that if option 1 is adopted then the probabilities of low, medium and high demand are 0.4, 0.5 and 0.1, respectively. For option 2 the respective probabilities are 0.1, 0.3 and 0.6 while for option 3 they are 0.05, 0.15 and 0.8. Determine the option which will lead to the highest expected profit. Would you have any reservations about recommending this option to the company?

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Profits ($000) Demand Option Low Medium High 1 -20 -20 100 2 -60 -20 60 3 -100 -60 20 62