Problem 1 (20 Points) Katrina is hosting a party to promote her new online marketing business. She has three options: 1. A huge gala event in a Convention Center salon 2. A medium sized event at a club house 3. A small event at a restaurant The costs of renting the place range from $500 (at the restaurant) to $8000 (at the Convention Center). Hosting the event at the club house costs $4000 the night. These prices only include an open bar for two hours. Dinner depends on the number of people that attend the event. The capacities and costs of dinner per person at each place also vary: 1. Restaurant: A maximum of 100 people and dinner per person is $20 2. Club House: A maximum of 300 people and dinner per person is $25 3. Convention Center: A maximum of 750 people and dinner per person is $20 Since she must make reservations beforehand, her situation is tight. She must decide several weeks ahead the place and make enough invitations to her target companies in the hope that she will get her invited parties to RSVP. After her invitees confirm, she will need to turn down some of them if her place is already capped. Suppose that for every person that attends, that will ensure at least $100 in sales for the next month. Demand is assumed to be discrete depending on whether some companies decide to attend. She estimated five companies; thus her demand options are: {50,150,300,500,750). These are all equally likely to occur. (a) Draw the decision tree that starts with the alternatives that Katrina has and that include the events that would occur (i.e., each demand option). Use payoff nodes where appropriate and probabilities. (10 points). (b) State the recommendation for Katrina that would maximize their profit. (5 points) (c) If she did not know the likelihood (probability) of the demand, what would be the best recommendation following the minimax regret criteria? (5 points)