Question

Your company has sent you on business to the Los Angeles (LA) metropolitan area. Upon your arrival at LAX, you make your way to the Klunker Car Rental counter. As usual, the line at the counter is long, so you enter and begin your wait. While waiting you notice that Klunker is offering a special deal on gas. They are selling gas for $1.579 per gallon. However, you must purchase a full tank when you rent the car. Klunker also says that the average price per gallon of gas in the LA area is $1.60. You are uncertain of several necessary pieces of information to determine whether you should take advantage of this deal. These are: · the total miles you will drive on the trip; · rental car gas mileage; · how much gas the rental car's tank holds; · the true cost of gas in the LA area. First, you expect to drive between 150 and 250 miles on this trip. You believe there is an equal chance that you will drive either of these extreme amounts. However, you may have to make a side trip to Edwards AFB that will increase the total miles to 500. You believe there is a 1 in 5 chance that this will happen. Normally, Klunker rents you a mid-size car. You believe most cars in this class have either a 15 gallon gas tank with 60% confidence or a 18 gallon gas tank with 40% confidence. You've heard that cars in this class get as much as 25 mpg on the highway but may get as little as 18 mpg city driving. You decide there is an 70% chance most of your driving will be on the freeways and the rest in the city. Finally, you don't believe Klunker's posted average price of $1.60 per gallon in the LA area. You guess that there is 40% chance that the gas will be $1.259, 20% chance it will be $1.479 and a 40% chance it will be $1.659. Assume you must decide whether to pre-purchase the tank of gas prior to talking to a Klunker clerk.

a. Draw the decision tree for this problem using Decision Tree in Excel.

b. What is the optimal decision?

c. Now suppose you can delay your decision until you speak to a clerk and find out exactly how much gas your rental car holds. The clerk says the car you will rent holds 18 gallons of gas. What is your optimal decision now? What is the value of this additional information?

*Please show steps in excel *

Answer 1

SOLUTION:

a.

The decision tree is a fully symmetric decision tree. The tree starts with the decision whether or not to purchase the full tank of gas. After the decision node are four event nodes for miles drive, miles per gallon realized, size of the fuel tank on the rental car, and the cost of gas in the LA area.
The following tables summarize the outcomes for each of the possible states of nature.

Purchase the tank

1.579

			Miles driven
MGP	TANK	Price	150	250	500
18	15	1.259	$23.69	$23.69	$39.77
18	15	1.479	$23.69	$23.69	$42.58
18	15	1.659	$23.69	$23.69	$44.88
18	18	1.259	$28.42	$28.42	$40.73
18	18	1.479	$28.42	$28.42	$42.88
18	18	1.659	$28.42	$28.42	$44.64
25	15	1.259	$23.69	$23.69	$29.98
25	15	1.479	$23.69	$23.69	$31.08
25	15	1.659	$23.69	$23.69	$31.98
25	18	1.259	$28.42	$28.42	$30.94
25	18	1.479	$28.42	$28.42	$31.38
25	18	1.659	$28.42	$28.42	$31.74

Purchase just the gas

				Miles Driven
MGP	TANK	Price	150	250	500
18	15	1.259	$10.49	$17.49	$34.97
18	15	1.479	$12.33	$20.54	$41.08
18	15	1.659	$13.83	$23.04	$46.08
18	18	1.259	$10.49	$17.49	$34.97
18	18	1.479	$12.33	$20.54	$41.08
18	18	1.659	$13.83	$23.04	$46.08
25	15	1.259	$7.55	$12.59	$25.18
25	15	1.479	$8.87	$14.79	$29.58
25	15	1.659	$9.95	$16.59	$33.18
25	18	1.259	$7.55	$12.59	$25.18
25	18	1.479	$8.87	$14.79	$29.58
25	18	1.659	$9.95	$16.59	$33.18

b.)

Based on the decision tree with the above outcomes included, the optimal decision is to purchase the tank of gas with an expected monetary value of $26.30.

c.)

If the decision is delayed until the clerk confirms there is an 18 gallon tank on the rental car, the decision remains the same. The expected monetary value increases to $29.6886 but since the decision has not changed this information has no value.