Jodi Wants To Lease A New Car And Start A Part-Time B 305520

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

Jodi aims to lease a new vehicle and establish a part-time transportation business to offer ride services. She engaged three automobile dealerships to compare leasing options, each offering a 36-month closed-end lease without an initial down payment. These leases include monthly payments, mileage allowances, and surcharges for exceeding the mileage limit.

While uncertain of her exact driving distance over the next three years, Jodi estimates three possible annual mileages: 10,000 miles, 14,000 miles, or 18,000 miles. Based on these assumptions, she calculated potential profits for each leasing option across the different mileages. The profit estimates from each dealer are summarized below:

Determine the best leasing decision for Jodi based on the following decision criteria:

• Maximax
• Maximin
• Equal likelihood (Laplace criterion)
• Minimax regret criterion

Paper For Above instruction

The decision to lease a vehicle for a small business involves analyzing multiple criteria to select the most advantageous option under uncertainty. Jodi faces three dealership options with different profit outcomes depending on her annual mileage. Applying decision-making criteria helps her determine the optimal choice, balancing risk and potential profit.

Maximax Criterion

The maximax criterion encourages selecting the option with the highest possible profit, emphasizing optimism. By reviewing each dealer’s maximum profit across the mileage scenarios:

• Dealer A: $13,500
• Dealer B: $11,500
• Dealer C: $10,000

According to maximax, Jodi should choose Dealer A, which offers the highest potential profit of $13,500. This criterion prioritizes the most optimistic outcome without regard to risk.

Maximin Criterion

The maximin approach considers the minimum profit for each dealer and selects the dealer with the highest of these minimums, emphasizing cautiousness. The minimum profits are:

• Dealer A: $7,000
• Dealer B: $8,500
• Dealer C: $9,500

Dealer C has the highest minimum profit at $9,500. Accordingly, the maximin decision suggests Jodi should lease from Dealer C to minimize potential loss, favoring security over maximum possible gain.

Equal Likelihood (Laplace Criterion)

The equal likelihood method assumes all scenarios are equally probable. The average profits for each dealer are calculated as:

• Dealer A: (7000 + 10500 + 13500) / 3 = $10,666.67
• Dealer B: (8500 + 11500 + 11000) / 3 = $10,666.67
• Dealer C: (10000 + 9500 + 9800) / 3 ≈ $9,766.67

Here, Dealers A and B tie with the highest average profit, suggesting either dealer could be the optimal choice based on this criterion.

Minimax Regret Criterion

This approach involves calculating regret for each decision in each state, which is the difference between the best payoff available in that state and the payoff for each decision. The steps include:

1. Identify the best profit in each state:
   • 10,000 miles: max profit is $10,000 (Dealer C)
   • 14,000 miles: max profit is $11,500 (Dealer B)
   • 18,000 miles: max profit is $13,500 (Dealer A)
2. Calculate regret for each dealer in each state:

   Dealer	10,000 miles	14,000 miles	18,000 miles
   A	$3,000 (10,000-7,000)	$1,000 (11,500-10,500)	$0 (13,500-13,500)
   B	$1,500 (10,000-8,500)	$0 (11,500-11,500)	$2,500 (13,500-11,000)
   C	$0 (10,000-10,000)	$2,000 (11,500-9,500)	$4,700 (13,500-8,800)

3. Determine the maximum regret for each dealer:
   • Dealer A: max regret is $3,000
   • Dealer B: max regret is $2,500
   • Dealer C: max regret is $4,700

Dealer B has the smallest maximum regret, indicating that leasing from Dealer B minimizes potential future regret based on uncertain profit scenarios.

Conclusion

Applying the different decision criteria yields different optimal choices: the maximax suggests Dealer A, maximin and minimax regret favor Dealer C and Dealer B respectively, and the equal likelihood points to Dealers A or B. Considering risk preferences, the conservatism of maximin and regret minimization might make Dealer B or C more attractive, while optimists might prefer Dealer A.

References

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