Max’s Bakery specializes in sourdough bread. A loaf of sourdough costs $2.00 to make and sells for a price of $4.00 in the store that day. All loaves not sold on the day that they are made are sold on the next day at $1.00 each.

Suppose that daily sourdough bread demand is either 20, 30, 40, or 50 loaves of bread, and Max also chooses between making 20, 30, 40 or 50 loaves each day.

Which of the following statements are true assuming Max uses the minimax regret strategy to make the baking decision?

Question

Max’s Bakery specializes in sourdough bread. A loaf of sourdough costs $2.00 to make and sells for a price of $4.00 in the store that day.  All loaves not sold on the day that they are made are sold on the next day at $1.00 each.

Suppose that daily sourdough bread demand is either 20, 30, 40, or 50 loaves of bread, and Max also chooses between making 20, 30, 40 or 50 loaves each day.

Which of the following statements are true assuming Max uses the minimax regret strategy to make the baking decision?

BlackTom AI · Accepted Answer

We’re evaluating a minimax regret problem for Max’s Bakery with four possible daily demands (20, 30, 40, 50) and four possible daily production quantities (20, 30, 40, 50). For each state (D) and decision (B), profit is revenue minus cost: Profit = 4*min(B,D) + 1*max(0,B-D) − 2*B. For each Demand level D, we compute the maximum achievable profit across all B, then the regret for each (B,D) as Regret(B,D) = max_profit_at_D − Profit(B,D). The largest regret across all D for a given B is the minimax regret for choosing that B; the minimax regret strategy selects the B that minimizes this worst-case regret. Below I evaluate each option in turn by looking at the computed regrets.

Option 1: “The regret for the decision of baking 20 loaves when 40 are demanded is $20.”
- When D = 40 and B = 20, from the calculations: Profit(20,40) = 40, and the max_profit_at_D for D = 40 is 80 (achieved with B = 40). Regret(20,40) = 80 − 40 = 40. This is not $20. Therefore this statement is incorrect.

Option 2: “The regret for the decision of baking 40 loaves when 20 are demanded is $20.”
- When D = 20 and B = 40, Profit(40,20) = 20, and the max_profit_at_D for D = 20 is 40 (achieved with B = 20). Regret(40,20) = 40 − 20 = 20. This matches $20, so this statement is correct.

Option 3: “The regret for the decision of baking 30 loaves when 50 are demanded is $20.”
- When D = 50 and B = 30, Profit(30,50) = 60, and the max_profit_at_D for D = 50 is 100 (achieved with B = 50). Regret(30,50) = 100 − 60 = 40, not $20. This statement is incorrect.

Option 4: “The regret for the decision of baking 50 loaves when 30 are demanded is $20.”
- When D = 30 and B = 50, Profit(50,30) = 40, and the max_profit_at_D for D = 30 is 60 (achieved with B = 30). Regret(50,30) = 60 − 40 = 20. This matches $20, so this statement is correct.

Option 5: “Exactly two answers are correct.”
- From the above, options 2 and 4 are correct, while 1 and 3 are incorrect. This would mean exactly two statements are correct. This statement is consistent with the computed results.

Option 6: “None of the answers are correct.”
- Since we found at least options 2 and 4 to be correct, this statement is false.

Summary of the option-by-option reasoning: the key numbers come from computing profits under each (B,D) pair, identifying the maximum profit for each D, deriving regrets as the gaps to that maximum, and then noting that the two specific regrets equal $20 are for (B=40, D=20) and (B=50, D=30). The two correct-statement pattern aligns with the existence of exactly two such $20 regrets across the presented choices, while the other listed regrets do not match $20.

类似问题

If the decisionmaker makes her decision based on the minimax regret approach, what is the maximum regret associated with this decision?

If the investor makes her decision based on the minimax regret approach, which decision should she take?

How did Egyptian culture and governance change during the Ptolemaic period compared to the pharaonic period?

Name the Supreme Court decision that removed financial constraints on PACs.

Political scientists Joshua Kalla and David Broockman find that senior policy makers made themselves available to _____ between three and four times more often than they did to constituents.

Name the political scientist who argues that parties are designed to serve the needs of ambitious politicians (namely candidates and officeholders).

Name the political scientist who said this famous quote about the problems of pluralism: “The flaw in the pluralist heaven is that the heavenly choir sings with a strong upper-class accent.”

What is the name of the third party candidate in 2000 who was not allowed to participate in the presidential debates? Hint: We watched a video clip with him in class.

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单