- For a decision analysis of this problem, what is the value in the opportunity loss (regret) table that corresponds to the action 'Rent Small Tent' and the state of nature 'Rain'?
Answer: $1,000
When you encounter a decision analysis problem involving opportunity loss (regret), you're calculating how much worse each decision performs compared to the best possible decision for each scenario.
To find the opportunity loss for "Rent Small Tent" when it "Rains," you first need to determine the net profit for each option in the rain scenario. Net profit equals revenue minus tent cost:
- Large tent: $10,000 revenue - $5,000 cost = $5,000 profit
- Small tent: $6,000 revenue - $2,000 cost = $4,000 profit
- No tent: $1,000 revenue - $0 cost = $1,000 profit
The best decision when it rains is renting the large tent ($5,000 profit). The opportunity loss for renting a small tent is the difference between the best possible outcome and the small tent outcome: $5,000 - $4,000 = $1,000.
Looking at the wrong answers: A) $2,000 is simply the cost of the small tent, not the opportunity loss. B) $4,000 is the actual profit from the small tent decision, not how much you lose by not choosing optimally. C) $5,000 is the profit from the optimal decision (large tent), but opportunity loss measures the gap between optimal and your chosen action.
The correct answer is D) $1,000.
Remember that opportunity loss always compares your chosen action against the best possible action for that specific scenario. It's not about costs or revenues directly—it's about the profit you're giving up by not making the optimal choice.
- A project manager is evaluating three software development approaches using a payoff table where values represent net present value in thousands of dollars. The equal likelihood criterion suggests Strategy 2, while the maximin criterion suggests Strategy 1. If Strategy 1 has payoffs of 20, 30, 40 and Strategy 3 has payoffs of 10, 35, 45, what can be concluded about Strategy 2's payoffs?
Answer: Strategy 2's minimum payoff is less than 20, and its average payoff exceeds 30
Since maximin criterion chooses Strategy 1, Strategy 1 must have the highest minimum payoff (20). Therefore, Strategy 2's minimum payoff must be less than 20. Since equal likelihood criterion chooses Strategy 2, it must have the highest average payoff. Strategy 1's average is 30, and Strategy 3's average is 30, so Strategy 2's average must exceed 30.
- A retailer is constructing a payoff table for ordering seasonal merchandise. She has three ordering options (Small, Medium, Large) and three possible demand scenarios. The payoffs are given as profits in hundreds of dollars. If the Medium order yields 15 under low demand, 25 under medium demand, and 30 under high demand, and the retailer wants to identify the strategy that maximizes the minimum possible payoff, what additional information is most critical for completing this analysis?
Answer: The payoffs for Small and Large order strategies under all demand scenarios
To apply the maximin criterion (maximize the minimum payoff), we need the complete payoff table showing all strategies under all scenarios. The maximin criterion only requires the payoff values, not probabilities (A), opportunity costs beyond those reflected in payoffs (C), or historical data (D).
- In the payoff table for this situation, what is the payoff corresponding to producing 100 units when market demand is 200 units?
Answer: $3,500
1. Calculate total revenue: All 100 units produced are sold. Revenue = 100 units * $70/unit = $7,000.
2. Calculate total cost: Production cost = 100 units * $30/unit = $3,000.
3. Calculate unmet demand: Demand (200) - Production (100) = 100 units.
4. Calculate penalty cost: 100 units unmet demand * $5/unit = $500.
5. Calculate final payoff (profit): Revenue - Production Cost - Penalty Cost = $7,000 - $3,000 - $500 = $3,500.
- In the payoff table for this decision, what is the payoff for the 'Launch' alternative if market adoption is 'Low'?
Answer: -$150,000
When analyzing payoff tables in decision theory, you need to understand that payoff represents the net financial outcome after considering all costs and revenues. This means you must subtract initial investments from any revenues generated.
For the 'Launch' decision with 'Low' market adoption, you need to calculate the net payoff by taking the revenue generated ($100,000) and subtracting the initial development cost ($250,000). This gives you: $100,000 - $250,000 = -$150,000. The negative value indicates a net loss.
Let's examine why the other options are incorrect. Choice A (-$250,000) represents only the initial cost without accounting for any revenue generated from the low adoption scenario. This ignores the $100,000 in revenue the app would still generate. Choice B ($100,000) is simply the gross revenue figure and fails to account for the initial development cost that must be recovered. Choice D ($50,000) appears to be a calculation error, possibly mixing up numbers or using incorrect arithmetic.
The key insight here is that payoff tables always show net outcomes, not gross revenues. Even when market adoption is low, the company still generates some revenue, but it's not enough to cover the initial investment, resulting in an overall loss.
Remember: in payoff calculations, always subtract all relevant costs from revenues to get the true financial position. Don't confuse gross revenue with net payoff – the initial investment must always be factored into your final calculation.
- A farmer constructs a payoff table for crop selection based on weather conditions, with payoffs representing profit per acre in dollars. The regret table shows that Crop A has regrets of 0, 50, 100 for dry, normal, and wet conditions respectively. If Crop B's payoffs are 200, 400, 300 for the same conditions, what is Crop A's payoff under normal weather conditions?
Answer: 350
Regret is calculated as (maximum payoff for that condition) minus (strategy's payoff for that condition). Crop A has 0 regret under dry conditions, meaning it achieves the maximum payoff for dry conditions. Crop A has 50 regret under normal conditions, and Crop B pays 400 under normal conditions. Since Crop A's regret is 50, the maximum payoff under normal conditions must be at least 400. If the maximum is 400 (from Crop B), then Crop A's payoff = 400 - 50 = 350.
- In the payoff table representing this problem, which value correctly represents the payoff for a specific crop under a specific weather condition?
Answer: The payoff for planting corn in Dry weather is $100.
The question requires correctly identifying an entry in the payoff table based on the text. A payoff table for this problem would have the crops (Corn, Soybeans, Wheat) as the alternatives (rows) and the weather conditions (Dry, Moderate, Wet) as the states of nature (columns). Reading the provided data:
- The profit for Corn if Dry is $100. This matches choice B.
- The profit for Soybeans in Wet weather is $130 (not $150). So A is incorrect.
- The profit for Wheat in Moderate weather is $140 (not $200). So C is incorrect.
- The profit for Corn in Wet weather is $50 (not $120). So D is incorrect.
- In the payoff table for this decision problem, what is the profit (payoff) if the bakery produces the large batch and the demand is low?
Answer: $850
To calculate the payoff for producing the large batch (80 cakes) with low demand (50 cakes):
1. Calculate the production cost: 80 cakes * $15/cake = $1200.
2. Calculate the revenue from sold cakes: 50 cakes * $40/cake = $2000.
3. Calculate the number of unsold cakes: 80 cakes produced - 50 cakes sold = 30 cakes.
4. Calculate the revenue from salvaged cakes: 30 cakes * $5/cake = $150.
5. Calculate total revenue: $2000 + $150 = $2150.
6. Calculate the profit (payoff): Total Revenue - Total Cost = $2150 - $1200 = $850.
- A logistics company evaluates three shipping strategies using a payoff table where entries represent cost savings in thousands of dollars. Strategy X dominates Strategy Y, and the minimax regret criterion selects Strategy Z. If Strategy X has the payoffs 40, 60, 80 and Strategy Z has payoffs 35, 70, 75, which statement about Strategy Y is necessarily true?
Answer: Strategy Y has all payoffs less than the corresponding payoffs of Strategy X
If Strategy X dominates Strategy Y, then Strategy X has payoffs that are greater than or equal to Strategy Y's payoffs in every state of nature, with at least one being strictly greater. This means all of Strategy Y's payoffs must be less than the corresponding payoffs of Strategy X (40, 60, 80).
