1. A state lottery pays $10,000 to anyone whose lottery ticket has a winning five digit lottery number. Any number from 00000 to 99999 is a possible winner and each ticket costs $1. What is the expected value of purchasing a ticket in this lottery? How much net revenue does the state expect, on average from each ticket? What is the risk preference of people who play this lottery? Explain.

1. You get a call from a business official in a school district.He needs assistance with a request from the school board.He has been asked to make a recommendation regarding the construction or renovation of the aging elementary school building.You have consulted with the grounds manager and a structural engineer and have been presented with two options.The district could build a new school building to replace the elementary school.You estimate that the cost to the district for the new building will be $3 million.Rather than building a new facility, the district could renovate the existing elementary school.A requirement for doing renovation is that the building must be brought into compliance with current building codes which have much more stringent structural requirements.The engineer has told you that there is a 60 percent chance that the renovation would require minimal structural repairs, in which case the total cost would be $1.5 million.There is a 40 percent chance that the renovation will end up requiring massive structural repairs resulting in a final project cost of $4 million.

a. Construct a decision tree for this problem using Excel.

c.Provide a one paragraph, written recommendation to the business official. In your recommendation be sure to outline the expected value, minimax and maximax decision strategies, and your reasoning behind your recommendation.

1. The Regional Alliance for the Homeless (RAH) runs an emergency shelter for homeless men in Upstate City.During the summer, fall, and spring when the weather is usually good, the shelter houses an average of 40 residents.The state reimburses RAH $50 per resident or about $2,000 per night for 40 residents.Expenses to run the shelter for 40 residents are about $1800 per night.

However, during stormy nights in the winter, the shelter gets full to its maximum legal capacity which is 80 residents.On these nights, the state still reimburses $50 per resident per night for a total reimbursement of $4000.In order to accommodate 80 clients, RAH has to open an overflow facility and put on double staffing, so its operating costs also double to $3,600.But here is the problem.If RAH puts on double staff and there is no storm, then only 40 residents will show up (gaining reimbursement of $2,000) and RAH will have to spend $3,600 for double staffing.But if RAH does not put on extra staff and 80 residents happen to show up, they will have to place them at the motel across the street at a cost of $80 per resident per night (that is 40 residents in the shelter and 40 residents go to the motel)quite a loss of funds.So the dilemma is to double staff or to go with regular staff during winter months.Furthermore, staffing schedules have to be set a week in advance before the weather can be reliably forecast.

(a) Construct a decision tree that you can use to analyze this situation.

(b). In the absence of any weather forecast, RAH knows that the long range probability of a storm on any day is 10%.So, assuming that Pr (Storm) = .1 during the winter, should RAH as a matter of routine policy work with regular staffing or double staffing during the winter?Note if there is any additional information that you need to solve this problem.

(c)Set up this problem making sure to break out any key parameters that may shift the final decision that the shelter would make.What are the key parameters and over what ranges, if any, do changes in these key parameters make a difference to the managers at RAH?