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ABC Products and XYZ Foods are the only two producers of salty snack crackers in Caracas. Each firm is considering two strategies to either increase sales or cut costs: ABC can reduce the size of its packaging or increase its advertising, and XYZ can issue coupons or reduce the quality of its ingredients.

The profits associated with each combination of these strategies, in thousands of dollars, are given in the payoff matrix shown below. The first entry represents ABC's payoff and the second entry represents XYZ's payoff.

[tex]\[
\begin{array}{|c|c|c|}
\hline
& \text{Coupon} & \text{Reduce Quality} \\
\hline
\text{Reduce Size} & \$10, \$60 & \$50, \$50 \\
\hline
\text{Advertise} & \$20, \$40 & \$40, \$20 \\
\hline
\end{array}
\][/tex]

Which strategy should each company choose to maximize their profits?

Sagot :

GinnyAnsweridn
Certainly! Let's break down the profits associated with each combination of strategies that ABC Products and XYZ Foods can implement.

### Strategies Overview

ABC Products has two strategies:
1. Reduce the size of its packaging.
2. Increase its advertising.

XYZ Foods also has two strategies:
1. Issue coupons to customers.
2. Reduce the quality of its ingredients.

### Payoff Matrix

The profits (in thousands of dollars) for both ABC Products and XYZ Foods for each combination of strategies are presented in a payoff matrix:

[tex]\[ \begin{array}{|c|c|c|} \hline ABC \backslash XYZ & \text{Coupon} & \text{Reduce Quality} \\ \hline \text{Reduce size} & (\$10, \$60) & (\$50, \$50) \\ \hline \text{Advertise} & (\$20, \$40) & (\$40, \$20) \\ \hline \end{array} \][/tex]

To understand this matrix:

- (\[tex]$10, \$[/tex]60) indicates:
- ABC Products earns \[tex]$10,000. - XYZ Foods earns \$[/tex]60,000.
- This happens when ABC Products reduces the size of its packaging and XYZ Foods issues coupons.

- (\[tex]$50, \$[/tex]50) indicates:
- ABC Products earns \[tex]$50,000. - XYZ Foods earns \$[/tex]50,000.
- This happens when ABC Products reduces the size of its packaging and XYZ Foods reduces the quality of its ingredients.

- (\[tex]$20, \$[/tex]40) indicates:
- ABC Products earns \[tex]$20,000. - XYZ Foods earns \$[/tex]40,000.
- This happens when ABC Products advertises and XYZ Foods issues coupons.

- (\[tex]$40, \$[/tex]20) indicates:
- ABC Products earns \[tex]$40,000. - XYZ Foods earns \$[/tex]20,000.
- This happens when ABC Products advertises and XYZ Foods reduces the quality of its ingredients.

### Summary

Combining the profits associated with each combination of these strategies, the payoff matrix for both firms is:

- Reducing the size of packaging and issuing coupons: (\[tex]$10, \$[/tex]60)
- Reducing the size of packaging and reducing quality: (\[tex]$50, \$[/tex]50)
- Increasing advertising and issuing coupons: (\[tex]$20, \$[/tex]40)
- Increasing advertising and reducing quality: (\[tex]$40, \$[/tex]20)

This information encapsulates the strategic choices and potential outcomes for both ABC Products and XYZ Foods.
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