UCLA Declining Population Stable Population and Growing Population Questions

Question Description

Problem 1

The manager of a construction company must decide whether to build single family homes, apartments, or condominiums. Profits (in thousands of dollars) are given in the following table and depend on various possible population trends. The probability of a declining population is 0.3, the probability for a stable population is 0.5 and the probability of a growing population is 0.2

Payoff table (in thousands of dollars):

	Declining Population	Stable Population	Growing Population
Single Family Homes	220	80	75
Apartments	85	175	100
Condominiums	-30	90	240

a)If the manager is an extreme optimist, which alternative would she choose?
b)If the manager is an extreme pessimist, which alternative would she choose?
c)If the manager wants to minimize maximum regret, which alternative should she choose?
d)If the manager wants to maximize expected values, which alternative should she choose?
e)What is the most amount of money that she should be willing to spend to get more information about the possible population trends?

Problem 2

Estimates of the financial information for a new product show the following information:

Fixed cost: $8,000

Variable cost: $6/unit

Revenue: $22/unit

The company assumes that the number of units sold will follow a normal distribution with a mean of 800 units and a standard deviation of 50 units.

Use the random numbers .51, .97, .58, .22, and .16 to conduct five trials of a Monte-Carlo simulation. What is the net profit for each trial? What is the average net profit over these 5 trials?

Use the following table to report your results:

Trial	Random Number	Units Sold	Net Profit
1	0.51
2	0.97
3	0.58
4	0.22
5	0.16
		Average

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