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.

MGMT 101 LEC ONL: MANA... Study Checkpoint 8: Decision Analysis I

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