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Zorluk: Çok zorExplaining Surprising Outcomes

A supermarket chain previously offered a "Buy One, Get One Free" (BOGO) promotion on its premium coffee brand exclusively on weekends, while charging the regular full price on weekdays. Recently, the chain eliminated the weekend BOGO promotion entirely and permanently reduced the regular price of the coffee by 50 percent every day of the week, accurately advertising that customers could now get the promotional per-unit price anytime. In the year following this pricing change, the total number of bags of this premium coffee sold by the chain increased by 20 percent compared to the prior year. Nevertheless, the chain's overall profit derived from this premium coffee dropped substantially, even though the wholesale cost per bag and all associated operational costs remained constant.

Which one of the following, if true, most helps to resolve the apparent discrepancy?

  1. A
    Although the total number of bags sold increased, the premium coffee constituted a significantly smaller percentage of the supermarket's total coffee sales following the pricing change.
  2. B
    The permanent price reduction successfully attracted many new customers who had never previously purchased the premium coffee, even during the weekend BOGO promotions.
  3. Prior to the pricing change, a substantial proportion of the supermarket's premium coffee sales occurred on weekdays, when customers purchased the coffee at the regular full price.Cevap
  4. D
    Under the new pricing model, the vast majority of the premium coffee is purchased by customers who buy only one bag at a time, whereas under the old model most customers bought two bags.
  5. E
    Many customers who regularly purchased the coffee during the weekend BOGO promotions believed that the promotion offered a better value than a standard 50 percent discount.

Cevap

The correct answer states that prior to the pricing change, a substantial proportion of the premium coffee sales occurred on weekdays at the regular full price.
The paradox asks us to explain how total profit declined despite a 20 percent increase in total volume and constant costs, given that the new permanent price (50 percent off) yields the exact same per-bag revenue as the old BOGO promotion. This discrepancy is resolved by recognizing that under the old system, not all bags were sold at the promotional BOGO price. The correct answer reveals that a substantial proportion of sales occurred on weekdays at full price. Under the new system, these high-margin full-price sales are replaced by discounted sales. The loss of the massive profit margin on these weekday sales mathematically outweighs the profit gained from the 20 percent increase in total volume, perfectly explaining the drop in total profit.

Adım Adım Çözüm

1
Analyze the financial mechanics of the pricing change.
A BOGO promotion effectively means customers pay 50% of the regular price per unit (buying 2 bags for the price of 1). The new pricing model permanently reduces the price to 50% for all units, meaning the profit per bag on discounted sales is identical in both scenarios.
To understand how revenue and profit per bag compare between the old and new promotional models.
2
Identify the core discrepancy.
Total bags sold increased by 20% and operational costs remained constant, yet total profit dropped substantially. Since the per-bag margin on discounted sales is identical in both models, the drop in total profit is mathematically paradoxical.
To pinpoint exactly what needs to be explained by the correct answer.
3
Formulate a hypothesis to resolve the paradox.
For total profit to drop despite a 20% volume increase and identical promotional margins, the supermarket must have lost a significant segment of sales that were previously occurring at a higher profit margin.
To establish the logical criteria for the correct answer.
4
Evaluate the options against the hypothesis.
The correct option reveals that under the old model, many sales occurred on weekdays at full price. The new model eliminated these high-margin sales, dragging down total profit despite the volume increase.
To select the mathematically and logically sound resolution.

Anahtar Kavram

Recognizing Hidden Subgroups and Margin Discrepancies in Averages
Tahmini Süre:2m 0s
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Explaining Surprising Outcomes

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