Consider two employees, Eddie and Urijah, working for a local construction company installing windows as well as sliding glass doors. The manager of the company is deciding how to allocate Eddie and Urijah's time throughout the workday with the goal of increasing overall productivity. The manager collected some baseline data and has taken note that in one 8 hour work day, Eddie can install 7 sliders OR 28 windows. That is, if Eddie spends the entire 8 hour work day installing windows, he can install 28 of them. Likewise, if Eddie spends the entire 8 hour work day installing sliders, he can install 7 of them. In contrast, in an 8 hour work day, Urijah can install either 21 sliders OR 42 windows
What is the opportunity cost associated with having Urijah install 1 slider?

To determine the opportunity cost associated with having Urijah install 1 slider, we need to understand the trade-off between installing sliders and windows for Urijah.

### Opportunity Cost

Opportunity cost is the value of the next best alternative that is foregone when a decision is made. In this context, the opportunity cost of installing sliders is the number of windows Urijah could have installed instead.

### Urijah's Productivity

Given:
- Urijah can install 21 sliders in an 8-hour workday.
- Urijah can install 42 windows in an 8-hour workday.

#### Calculate the Opportunity Cost

1. **Calculate the rate of installation per slider and per window:**

   - **Sliders:** Urijah installs 21 sliders in 8 hours.
     \[
     \text{Time per slider} = \frac{8 \text{ hours}}{21 \text{ sliders}} = \frac{8}{21} \text{ hours per slider}
     \]

   - **Windows:** Urijah installs 42 windows in 8 hours.
     \[
     \text{Time per window} = \frac{8 \text{ hours}}{42 \text{ windows}} = \frac{8}{42} \text{ hours per window} = \frac{4}{21} \text{ hours per window}
     \]

2. **Calculate the opportunity cost of 1 slider:**

   - If Urijah spends \(\frac{8}{21}\) hours installing 1 slider, he cannot use this time to install windows.

   - Determine how many windows Urijah can install in the time it takes to install 1 slider:
     \[
     \text{Windows per slider} = \frac{\text{Time per slider}}{\text{Time per window}} = \frac{\frac{8}{21}}{\frac{4}{21}} = \frac{8}{4} = 2
     \]

Therefore, the opportunity cost of having Urijah install 1 slider is 2 windows.

### Conclusion

- **Opportunity Cost for Urijah to install 1 slider:** 2 windows

If you have further questions or need additional details, feel free to ask!

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### Additional Questions:

1. What is the opportunity cost for Urijah to install 1 window instead?
2. What is the opportunity cost for Eddie to install 1 slider?
3. How does the opportunity cost differ between Eddie and Urijah for sliders?
4. How would the opportunity costs change if Eddie could install 10 sliders in a day?
5. How many total sliders and windows can Eddie and Urijah install together in one workday if they both specialize in one task?
6. How does opportunity cost impact decision-making in business?
7. What other factors should the manager consider when allocating tasks between Eddie and Urijah?
8. What are the benefits of understanding opportunity costs in a production setting?

**Tip:** When analyzing opportunity costs, consider both qualitative factors (like skill levels and preferences) and quantitative ones (like time and resource constraints) to make the most informed decision.

Explore how to calculate opportunity cost in productivity using Urijah's slider installation impact. Understand the trade-offs between sliders and windows installation and its implications on overall productivity. Suitable for advanced high school and college-level students.

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