# Decision Analysis » Problem-01 Solution | Operations Research

Problem-01: A marketing agent frequently flies from Montreal to Boston. She can ride the airport bus from her hotel to the airport, which costs \$3; but if she takes it, there is a .08 chance that she will miss the flight. A hotel limousine costs \$7, with a .96 chance of being on time for the flight. For \$15, she can take a taxi that will make 99 of 100 flights. Each time she catches the plane, she will conclude a business transaction that will produce a profit of \$1,000; otherwise, she will lose the deal. Which mode of transportation should the marketing agent use in order to maximize her profits?

Solution:
According to given data, we can draw following decision tree:
 Figure: Decision Tree, according to given data.

Net Profit Calculation from different mode of transportation:

For Airport Bus :

EMV=\$1,000 (.92) + \$0 (.08) = \$920
Net Profit: \$920 - \$3 = \$917

For Hotel Limousine :

EMV=\$1,000 (.96) + \$0 (.04) = \$960
Net Profit: \$960 - \$7 = \$953

For Taxi :

EMV=\$1,000 (.99) + \$0 (.01) = \$990
Net Profit: \$990 - \$15 = \$975

 Figure: Decision Tree for making final decision.
Here, Taxi, represents the highest profit from others. Since, the marketing agent should use a taxi in order to maximize her profits.

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