Carter Racing is in a difficult situation with respect to determining whether to enter an upcoming race at Pocono. On the one hand, in the event of a favorable performance Carter Racing stands to gain a $1 million sponsorship with Goodstone Tires that could finance Carter Racing to add another car next season. On the other hand, in the event of a poor performance Carter Racing risks losing an existing oil sponsorship worth $500,000 that is critical to next year’s race season. After careful analysis, however, I believe that Carter Racing should enter the Pocono race because it stands to gain more by doing so than it stands to lose.
Temperature is the main factor that comes into play. Low ambient temperatures wreak havoc on the car’s gasket and force Carter Racing to abandon races early. This becomes readily apparent when temperatures below 60° are plotted against gasket failures, as in the figure below. Variance in this case is calculated as .6447, which means that the independent variable (temperature) has a 65% effect on the dependent variable (gasket failure). Note that temperatures above 60° are ignored from this analysis because cool temperatures are forecast for race day; consequently, an analysis of high temperatures is irrelevant.
Using the information calculated above (R2 = 0.6447), one can build a decision tree to determine algebraically the optimal course of action. Carter Racing faces a 65% chance of not completing a race in cool temperatures; and by extension it only has a 35% chance of finishing a race under such conditions. However, the payoff associated with completing a race ($1.5 million consisting of the tire contract and the oil contract) exceeds the prospective loss of retiring from the event ($500K associated with the oil contract). When one combines the weighted probabilities of both events occurring to the associated dollar amounts, the end result of $200K exceeds the $50K loss attributed to skipping the event. As a result, Carter...
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