# 8.4.8 R8. Google AdWords - Video 7: Sensitivity Analysis | Summary and Q&A

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December 13, 2018
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MIT OpenCourseWare

## TL;DR

This video explores how to use a linear optimization model to answer "what if" questions and conduct sensitivity analysis.

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### Q: How can a linear optimization model be used to answer "what if" questions?

A linear optimization model allows for changing data values and observing how the solution and objective value respond to these changes. By varying inputs, we can analyze the impact of different scenarios on the optimal solution.

### Q: What is the relationship between click-through-rate and average price per display?

The average price per display is calculated by multiplying the click-through-rate with the price-per-click. Increasing the click-through-rate will lead to a corresponding change in the average price per display.

### Q: Why didn't increasing AT&T's budget result in a change in the solution?

The previous solution did not fully utilize AT&T's budget, meaning that the constraint was not binding. Increasing the budget beyond the previously used amount does not have an effect on the solution in this case.

### Q: What determines the maximum revenue that can be attained in this optimization model?

The sum of the budgets for each advertiser represents the maximum revenue achievable because Google earns from each advertiser only what they spend. If the sum of the budgets is the highest possible expenditure, then the revenue will also be maximized.

## Summary & Key Takeaways

• The video demonstrates how to use a spreadsheet to change data values and observe the corresponding changes in the solution and objective value.

• It showcases an example of increasing the click-through-rate for AT&T with query one and analyzes the effects on the average price per display, solution allocations, and revenue.

• Another example is given, where the budget for AT&T is increased, but the solution remains unchanged due to the constraint not being binding.