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Time Remaining 2 hours 52 minutes 27 seconds

**02:52:27**

If a vendor has correctly used marginal analysis to select its stock levels for the day (as in the newsperson problem in the text), and if the profit resulting from the last unit being sold (*Cu*) is $120 and the loss resulting from that unit if it is not sold (*Co*.) is $360, which of the following is the probability of the last unit being sold?

Multiple Choice

Greater than 0.90

Greater than 0.15

Greater than 0.75

Greater than 0.85

Greater than 0.25

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The problem you've presented is related to the "newsvendor problem," where a vendor must decide how much stock to order based on uncertain demand. The key variables are:

- **Cu**: Profit from selling the last unit (here, $ Cu = 120 $)
- **Co**: Cost or loss if the last unit is unsold (here, $ Co = 360 $)

The formula used to determine the optimal probability, known as the critical ratio (CR), is given by:

\[
CR = \frac{Cu}{Cu + Co}
\]

Now, let's plug in the values provided:

\[
CR = \frac{120}{120 + 360} = \frac{120}{480} = 0.25
\]

This means that the vendor should stock such that the probability of selling the last unit is **25%**.

The correct answer is:
- **Greater than 0.25**

Would you like further explanation on marginal analysis or any additional details?

Here are 5 related questions to deepen your understanding:
1. How does the critical ratio change if the profit from the last unit increases?
2. What would happen if the cost of unsold items exceeds the profit from sold items?
3. How does the newsvendor model apply in real-world scenarios?
4. How can vendors use marginal analysis to avoid stockouts or overstocking?
5. What are other factors (besides probability) that influence a vendor’s decision?

**Tip:** Always double-check how **Cu** and **Co** impact the critical ratio. Higher values for $ Cu $ increase the likelihood of stocking more units.

If a vendor has correctly used marginal analysis to select its stock levels for the day (as in the newsperson problem in the text), and if the profit resulting from the last unit being sold (Cu) is $120 and the loss resulting from that unit if it is not sold (Co) is $360, which of the following is the probability of the last unit being sold?

Learn how to calculate the probability of the last unit being sold in the newsvendor problem using marginal analysis. With a profit of $120 and a loss of $360, we use the critical ratio formula to determine the optimal stock levels. This problem is suitable for undergraduate business or economics students.

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