1. **Problem Statement:** We need to find the price of a basic subscription and a premium subscription given the revenue function and contour lines on the graph.
2. **Understanding the Revenue Function:** The revenue $R$ is given by
$$R = \text{price\_basic} \times c + \text{price\_premium} \times d,$$
where $c$ is the number of basic subscribers and $d$ is the number of premium subscribers.
3. **Analyzing the Graph:** The contour lines represent constant revenue values: 1000, 2000, 3000, 4000, and 5000.
4. **Interpreting Contour Spacing:** The increase from 1000 to 2000 corresponds to an increase of 1000 in revenue.
5. **Horizontal Movement (change in $c$):** Moving horizontally by 50 units in $c$ (with $d$ fixed) increases revenue by 1000.
6. **Vertical Movement (change in $d$):** Moving vertically by 100 units in $d$ (with $c$ fixed) also increases revenue by 1000.
7. **Calculating Price of Basic Subscription:** Since increasing $c$ by 50 increases revenue by 1000,
$$\text{price\_basic} = \frac{1000}{50} = 20.$$
8. **Calculating Price of Premium Subscription:** Since increasing $d$ by 100 increases revenue by 1000,
$$\text{price\_premium} = \frac{1000}{100} = 10.$$
9. **Final Answer:**
- Price of basic subscription = 20
- Price of premium subscription = 10
This means each basic subscriber contributes 20 dollars to revenue, and each premium subscriber contributes 10 dollars.
Subscription Prices
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