Questions: For what values of X will Germany export cars and import wine? (Check all that apply.) □ 900 □ 820 □ 1 □ 950 □ 900 □ 820 □ 800 For what values of X will Germany import cars and export wine? (Check all that apply.) A German worker takes 600 hours to produce a car and X hours to produce a wine.

To determine for what values of X Germany will export cars and import wine, and for what values of X Germany will import cars and export wine, we need to compare the opportunity costs of producing cars and wine in Germany with those in another country. However, since the problem does not provide information about the other country's production times, we will assume that Germany will export the good for which it has a lower opportunity cost and import the good for which it has a higher opportunity cost.

Let's calculate the opportunity cost for Germany:

1. Opportunity Cost of Producing Cars in Germany:

   • A German worker takes 600 hours to produce a car.
   • If X hours are required to produce a unit of wine, the opportunity cost of producing one car is \( \frac{600}{X} \) units of wine.

2. Opportunity Cost of Producing Wine in Germany:

   • A German worker takes X hours to produce a unit of wine.
   • The opportunity cost of producing one unit of wine is \( \frac{X}{600} \) cars.

Germany will export cars and import wine if the opportunity cost of producing cars in Germany is lower than the opportunity cost of producing cars in the other country. Conversely, Germany will import cars and export wine if the opportunity cost of producing wine in Germany is lower than the opportunity cost of producing wine in the other country.

Without the other country's data, we can only determine the relative opportunity costs within Germany. Let's assume that the other country has a fixed opportunity cost for producing cars and wine, and we need to find the values of X that make Germany's opportunity costs favorable for exporting cars or wine.

For Germany to export cars and import wine:

• The opportunity cost of producing cars in Germany should be lower than the opportunity cost of producing wine.
• \( \frac{600}{X} < \frac{X}{600} \)
• Solving this inequality: \[ 600^2 < X^2 \] \[ 360000 < X^2 \] \[ X > 600 \]

For Germany to import cars and export wine:

• The opportunity cost of producing wine in Germany should be lower than the opportunity cost of producing cars.
• \( \frac{X}{600} < \frac{600}{X} \)
• Solving this inequality: \[ X^2 < 360000 \] \[ X < 600 \]

Now, let's check the given values of X:

• 900: \( X > 600 \) (Germany exports cars and imports wine)
• 820: \( X > 600 \) (Germany exports cars and imports wine)
• 1: \( X < 600 \) (Germany imports cars and exports wine)
• 950: \( X > 600 \) (Germany exports cars and imports wine)
• 900: \( X > 600 \) (Germany exports cars and imports wine)
• 820: \( X > 600 \) (Germany exports cars and imports wine)
• 800: \( X > 600 \) (Germany exports cars and imports wine)

Summary:

For what values of X will Germany export cars and import wine? (Check all that apply.)

• 900
• 820
• 950
• 900
• 820
• 800

For what values of X will Germany import cars and export wine? (Check all that apply.)

• 1