### MATH 318, Decision Tree Worksheet

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This worksheet is based on problem 12 in Chapter 4 of Quantitative Methods for Business.
Air Express has said they will consider moving their headquarters to Potsdam if Potsdam agrees to extend the runway of its airport. The town estimates that if the runway is lengthened there is a 40% chance of Air Express moving their headquarters.

In addition, DRI is considering locating a warehouse in Potsdam. DRI is more likely to build a warehouse in Potsdam if Air Express is headquartered there (75% probability vs. 67% probability of building).

The cost to extend the runway is \$200,000. The projected 5 year revenue from Air Express moving its headquarters is \$350,000. The projected 5 year revenue from the DRI warehouse is \$450,000.

1. Is it worth extending the runway just for the 40% chance of attracting Air Express? Draw a decision tree (omitting any mention of DRI) and use it to calculate an answer. Don't forget to include the \$200,000 cost in the payoff for Air Express relocation.

2. Create a new decision tree which includes the possibility that DRI will build a warehouse in Potsdam. (Will DRI make their decision about the warehouse before or after Air Express decides on their headquarters' location?) Use that decision tree to determine whether Potsdam should extend the runway.

3. DRI says they'd be more likely to relocate if Potsdam changed the zoning near the airport (67% probability increases to 80%). The cost to change the zoning is estimated to be \$50,000.  If Potsdam decides not to extend the runway, they will consider a zoning change.  Copy your decision tree from the previous problem and add this decision node to the tree.

4. Use your decision tree to describe the optimal decision strategy for the town of Potsdam.

Bonus (5 points) Ignoring the option to change zoning near the airport, what do the optimistic and conservative decision making strategies recommend for the town of Potsdam? Explain your answer.