https://file.aiquickdraw.com/mathbot/file/1730752638263elday2on.jpg

Let's analyze the exercise based on the provided image:

### Problem Summary:
A company manufactures objects each day. 
- \( x \): number of objects produced per day.
- \( C \): production cost in euros for \( x \) objects, represented by curve \( C \).
- \( R \): revenue in euros for \( x \) objects, represented by curve \( R \).

### Questions Analysis:
1. **For how many objects are the revenues greater than 25,000 euros?**
   - We need to find the \( x \)-value range where the revenue curve \( R \) is above 25,000 euros on the graph.

2. **For how many objects is the production cost above 15,000 euros?**
   - We need to find the \( x \)-value range where the cost curve \( C \) exceeds 15,000 euros.

3. **For how many objects are the revenues equal to the costs?**
   - This corresponds to the intersection points between curves \( C \) and \( R \).

4. **For what quantity of objects is the company profitable?**
   - Profitability occurs when revenues \( R \) exceed costs \( C \), so we need to identify the \( x \)-values where \( R > C \).

5. **How many objects should be produced to maximize the company's profits?**
   - To find the optimal production quantity, we need to locate the point where the difference \( R - C \) is maximized.

Would you like a detailed step-by-step approach to solve each of these questions? 

---

#### Related Questions to Deepen Understanding:
1. How do you determine the profitability threshold from a cost and revenue graph?
2. What is the significance of the intersection points between cost and revenue curves?
3. How does maximizing profit differ from simply achieving profitability?
4. What are other potential factors affecting profitability beyond the revenue and cost curves?
5. Why might a company choose to produce fewer items even if higher production maximizes profit?

#### Tip:
In graph analysis, always pay attention to the scales on both axes to ensure accurate interpretation of values.

Une entreprise fabrique chaque jour des objets. On note x le nombre d'objets fabriqués par jour. Le coût de production en euros de x objets est noté C et est représenté par la courbe C. On note R, les recettes en euros pour x objets fabriqués.

1) Pour combien d'objets fabriqués les recettes sont-elles supérieures à 25 000 euros ?
2) Pour combien d'objets fabriqués le coût de production est supérieur à 15 000 euros ?
3) Pour combien d'objets fabriqués les recettes sont-elles égales aux coûts ?
4) Pour quelle(s) quantité(s) d’objet l’entreprise est-elle rentable ?
5) Combien d’objets faut-il produire pour maximiser les bénéfices de l’entreprise ?

Analyze the production cost and revenue graph to determine profitability and optimal production levels for a company. Explore concepts such as graph intersections, cost, revenue, and profit maximization. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation