Jodi Wants To Lease A New Car And Start A Part-Time B 318104

Jodi Wants To Lease A New Car And Start a Part Time Business To Giv

Jodi is considering leasing a new car with plans to start a part-time business offering rides. She has obtained pricing information from three automobile dealers, each offering a 36-month closed-end lease with no initial down payment. The leases include a monthly fee, a mileage allowance, and charges for additional miles driven beyond the allowance. Jodi anticipates that her annual miles will be approximately 10,000, 14,000, or 18,000 miles, which will influence her total profit based on each leasing option. The estimated profits for each dealer under different mileage scenarios are as follows:

  • Dealer A: 10,000 miles - $7,000; 14,000 miles - $10,500; 18,000 miles - $13,500
  • Dealer B: 10,000 miles - $8,500; 14,000 miles - $11,500; 18,000 miles - $11,000
  • Dealer C: 10,000 miles - $10,000; 14,000 miles - $9,500; 18,000 miles - $9,800

Determine the best leasing decision based on various decision criteria: maximax, maximin, equal likelihood, and minimax regret. Additionally, evaluate the decision using the probabilities provided (P(10,000 miles) = 0.5, P(14,000 miles) = 0.3, P(18,000 miles) = 0.2) by calculating the expected value, the expected regret, and the expected value of perfect information. Provide detailed calculations and interpretations for each criterion.

Paper For Above instruction

In the context of Jodi’s leasing decision, applying decision analysis methods enables her to select the optimal lease option under uncertainty. Each decision criterion offers a different perspective. The maximax approach aims to maximize potential gains by selecting the choice with the highest possible profit, assuming the best-case scenario for each dealer. Conversely, the maximin criterion emphasizes caution by choosing the option with the highest minimum profit across all scenarios, prioritizing safety over maximum potential reward. The equal likelihood method assigns probabilities equally, evaluating the expected profit based on these assumptions. Finally, the minimax regret focuses on minimizing potential regret, which involves calculating the regret for each decision and selecting the one with the smallest maximum regret.

Applying the maximax criterion, Dealer C provides the highest maximum profit of $10,000, making it the preferred choice under this approach. The maximin criterion, however, considers the minimum profits: Dealer A has the highest minimum at $7,000, suggesting Dealer A by this measure. The equal likelihood method weighs the profits according to the assigned probabilities, leading to the expected values of:

  • Dealer A: (0.5$7,000 + 0.3$10,500 + 0.2*$13,500) = $9,400
  • Dealer B: (0.5$8,500 + 0.3$11,500 + 0.2*$11,000) = $10,150
  • Dealer C: (0.5$10,000 + 0.3$9,500 + 0.2*$9,800) = $9,850

Based on these calculations, Dealer B offers the highest expected profit under equal probability assumptions. To evaluate the minimax regret, first, construct a regret table by subtracting the profit of each decision from the maximum profit in each scenario. The maximum profits across scenarios are for Dealer C at all mileage levels. The regret table indicates that Dealer A's maximum regret is $3,500, Dealer B's is $2,500, and Dealer C's is $2,200, indicating Dealer C is preferred when minimizing regret.

Considering the probabilities, the expected values indicate Dealer B as the most favorable decision, as it provides the highest expected profit of $10,150. The expected regret calculation reinforces this, as Dealer B exhibits the lowest maximum regret. The value of perfect information can be computed by assessing the expected profit if Jodi knew exactly which mileage scenario would occur, thus avoiding any decision regret. This value helps her determine whether investing in additional information or analysis justifies the potential benefit.

Decision Analysis and Recommendations

In summary, depending on Jodi’s risk preferences, different decisions emerge as optimal. The maximax method favors Dealer C for maximum potential profit, whereas the maximin favors Dealer A for safety. The probabilistic approach favors Dealer B under expected value calculations, aligning with a balanced risk-reward perspective. The regret analysis further supports choosing Dealer B. Therefore, given the probability weights and potential benefits, Jodi should consider leasing from Dealer B based on expected value and regret minimization, but she should also consider her risk tolerance when making her final decision.

References

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