A firm producing lamps has fixed costs of €1000 per week. A lamp costs €15 to produce. (a) Write down the equation for total cost.
(b) Graph the total cost function for Q = 0 to 100.
(c) Calculate the cost of producing 25 lamps.
(d) How many lamps are produced when total costs are €7000?

Here is the graph of the total cost function \(TC = 1000 + 15Q\) for \(Q\) ranging from 0 to 100 lamps.

### (c) Calculate the Cost of Producing 25 Lamps

To find the total cost of producing 25 lamps, substitute \(Q = 25\) into the total cost equation:

\[
TC = 1000 + 15 \times 25 = 1000 + 375 = 1375 \,€
\]

So, the total cost of producing 25 lamps is €1375.

### (d) How Many Lamps Are Produced When Total Costs Are €7000?

We need to solve for \(Q\) when the total cost is €7000:

\[
7000 = 1000 + 15Q
\]

Subtracting 1000 from both sides:

\[
6000 = 15Q
\]

Dividing both sides by 15:

\[
Q = \frac{6000}{15} = 400
\]

Thus, 400 lamps are produced when the total costs are €7000.

---

Would you like more details or have any questions about the solutions? Here are some related questions for further exploration:

1. What is the break-even point where total costs equal total revenue?
2. If the price per lamp sold is €20, how much profit is made at 50 lamps?
3. How does the total cost change if the fixed cost increases to €1200 per week?
4. What is the marginal cost of producing one more lamp?
5. How does the total cost function change if variable costs per lamp increase to €18?

**Tip**: When analyzing cost functions, always differentiate between fixed and variable costs to better understand the firm's cost structure.

A firm producing lamps has fixed costs of €1000 per week. A lamp costs €15 to produce. (a) Write down the equation for total cost. (b) Graph the total cost function for Q = 0 to 100. (c) Calculate the cost of producing 25 lamps. (d) How many lamps are produced when total costs are €7000?

Explore how to calculate the total cost function for a firm producing lamps with €1000 fixed costs and €15 per lamp. Learn to graph the cost function, calculate costs for 25 lamps, and determine how many lamps are produced when total costs reach €7000. Suitable for Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation