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Yaster Inc. is trying to enter the thingamabob market.  The research department established the following price-demand, cost, and revenue functions:

where x is in thousands of thingamabobs and C(x) and R(x) are in thousands of dollars.  The price p(x) is the price in dollars of one thingamabob when the demand is x thousand thingamabobs.  All three functions have domain 1≤x≤50.

Use this information to answer the questions below.

The graph you've uploaded appears to show a quadratic function with a parabolic shape, which suggests that this could represent a function related to cost or revenue, as those functions often exhibit this form in economics and business optimization problems. However, the specific problem you're referring to with functions like price-demand, cost, and revenue requires more concrete details, such as the actual functional forms of \( C(x) \), \( R(x) \), and \( p(x) \).

To assist you more effectively, I'll need clarification on these functions. Typically, the price-demand function, cost function, and revenue function follow these formats:

- **Price-demand function**: \( p(x) \) gives the price per unit when \( x \) units are demanded.
- **Cost function**: \( C(x) \) gives the total cost to produce \( x \) units.
- **Revenue function**: \( R(x) = p(x) \cdot x \), which gives total revenue from selling \( x \) units.

If you can provide the equations or additional details related to these functions, I can help calculate key metrics like break-even points, profit maximization, or price elasticity. Let me know if you'd like help with this.

Would you like to share more information, or should we proceed with analyzing the graph directly? Here are a few specific questions that might help guide the next step:

1. What is the specific equation for the price-demand function \( p(x) \)?
2. What is the cost function \( C(x) \)?
3. Do you need to find maximum revenue or profit?
4. Are you looking for break-even points or other specific values?
5. Would you like help interpreting the graph?

**Tip**: In business problems, revenue is often maximized when the price per unit (from the price-demand function) balances perfectly with the number of units sold.

Let me know how you'd like to proceed!

Yaster Inc. is trying to enter the thingamabob market. The research department established the following price-demand, cost, and revenue functions where x is in thousands of thingamabobs, and C(x) and R(x) are in thousands of dollars. The price p(x) is the price in dollars of one thingamabob when the demand is x thousand thingamabobs. All three functions have domain 1≤x≤50. Use this information to answer the questions below.

Explore the price-demand, cost, and revenue functions for Yaster Inc. as they enter the thingamabob market. Understand how to calculate maximum revenue, break-even points, and optimize production within the domain 1 ≤ x ≤ 50 (in thousands of thingamabobs). This lesson includes key quadratic functions, algebra, and business optimization concepts.

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