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 one of those quantities. Suppose the probabilities corresponding to the demands of 20, 30, 40, and 50 loaves are 0.2, 0.3, 0.3, and 0.2, respectively

Which of the following statements are true assuming Max uses the expected monetary value (EMV) 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 one of those quantities.  Suppose the probabilities corresponding to the demands of 20, 30, 40, and 50 loaves are 0.2, 0.3, 0.3, and 0.2, respectively

Which of the following statements are true assuming Max uses the expected monetary value (EMV) strategy to make the baking decision?

BlackTom AI · Accepted Answer

Let’s parse the problem carefully and lay out how profit is computed for any chosen production quantity.
For a given day, Max decides to bake q loaves (q ∈ {20, 30, 40, 50}). Demand D can be 20, 30, 40, or 50 with probabilities 0.2, 0.3, 0.3, 0.2 respectively. Each loaf costs 2 to make and sells for 4 if sold that day. Unsold loaves (q − min(q, D)) can be sold the next day at 1 each.
Profit is revenue minus cost. A compact way to write total profit for a given q and realized D is:
Profit = 4·min(q, D) + 1·(q − min(q, D)) − 2q
= 3·min(q, D) + q − 2q
= 3·min(q, D) − q.
Thus the EMV for a particular q is the weighted average of 3·min(q, D) − q over all possible D using their probabilities.
Now evaluate each option by computing the EMV for each q.

Option 1: Best decision is bake 30 loaves.
- Compute min(q, D) for q = 30: when D = 20, min = 20; when D = 30, min = 30; when D = 40, min = 30; when D = 50, min = 30.
- Profit values: for D=20: 3·20 − 30 = 60 − 30 = 30; D=30: 3·30 − 30 = 90 − 30 = 60; D=40: 3·30 − 30 = 60; D=50: 3·30 − 30 = 60.
- EMV = 0.2·30 + 0.3·60 + 0.3·60 + 0.2·60 = 6 + 18 + 18 + 12 = 54.
Since this EMV (54) is not necessarily the highest among all q (see below), this option’s blanket claim that 30 is the best is unlikely to hold.

Option 2: EMV of the best decision is $54.
- From the calculations above, the EMV for q = 30 is 54, but we must check all q. For q = 20, min(q, D) = 20 for all D, giving Profit = 3·20 − 20 = 40, so EMV = 40. For q = 40, mins are 20, 30, 40, 40 with profits 20, 50, 80, 80, leading to EMV = 0.2·20 + 0.3·50 + 0.3·80 + 0.2·80 = 4 + 15 + 24 + 16 = 59. For q = 50, mins are 20, 30, 40, 50 with profits 10, 40, 70, 100, giving EMV = 0.2·10 + 0.3·40 + 0.3·70 + 0.2·100 = 2 + 12 + 21 + 20 = 55.
- The best EMV among these is 59 (for q = 40), not 54. Therefore this statement is not correct.

Option 3: There is a tie between two decisions with respect to the best EMV.
- From the computed EMVs: q = 20 → 40, q = 30 → 54, q = 40 → 59, q = 50 → 55. None are equal to 59 except q = 40, and no other q shares 59. There is no tie for the best EMV.
- Hence this option is false.

Option 4: The difference between the decisions with best and worst EMVs is $19.
- The worst EMV is 40 (q = 20). The best EMV is 59 (q = 40).
- Difference = 59 − 40 = 19. This matches the statement, so this option appears consistent with the computed values.

Option 5: Exactly two answers are correct.
- From the analysis above, only the fourth option aligns with the computed EMVs and there isn’t a second option that is correct. Therefore this statement is false.

Option 6: None of the answers are correct.
- Since option 4 is correct, this statement is false.

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

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