To solve the problem step by step, follow these instructions:

1. **Understand the given equations:**
- Cost function: $ C = 4n + 2400 $
- Revenue function: $ R = 6n $
- Here, $ n $ represents the number of baskets produced.

2. **Sketch the graphs of $ C $ and $ R $:**
- The cost function $ C = 4n + 2400 $ is a linear equation with a slope of 4 and a y-intercept of 2400.
- The revenue function $ R = 6n $ is a linear equation with a slope of 6 and a y-intercept of 0.

3. **Plot the cost function $ C $:**
- Start at the y-intercept (0, 2400).
- Use the slope to find another point. For example, when $ n = 100 $:
$$
C = 4(100) + 2400 = 400 + 2400 = 2800
$$
- Plot the point (100, 2800) and draw a line through the points (0, 2400) and (100, 2800).

4. **Plot the revenue function $ R $:**
- Start at the origin (0, 0).
- Use the slope to find another point. For example, when $ n = 100 $:
$$
R = 6(100) = 600
$$
- Plot the point (100, 600) and draw a line through the points (0, 0) and (100, 600).

5. **Determine the number of baskets produced when costs equal revenue:**
- Set the cost function equal to the revenue function:
$$
4n + 2400 = 6n
$$
- Solve for $ n $:
$$
2400 = 6n - 4n
$$
$$
2400 = 2n
$$
$$
n = \frac{2400}{2} = 1200
$$

6. **Conclusion:**
- The number of baskets produced when costs equal revenue is $ n = 1200 $.

By following these steps, you can sketch the graphs of the cost and revenue functions and determine that the number of baskets produced when costs equal revenue is 1200.

Question

To solve the problem step by step, follow these instructions:

1. **Understand the given equations:**
   - Cost function: $ C = 4n + 2400 $
   - Revenue function: $ R = 6n $
   - Here, $ n $ represents the number of baskets produced.

2. **Sketch the graphs of $ C $ and $ R $:**
   - The cost function $ C = 4n + 2400 $ is a linear equation with a slope of 4 and a y-intercept of 2400.
   - The revenue function $ R = 6n $ is a linear equation with a slope of 6 and a y-intercept of 0.

3. **Plot the cost function $ C $:**
   - Start at the y-intercept (0, 2400).
   - Use the slope to find another point. For example, when $ n = 100 $:
     $$
     C = 4(100) + 2400 = 400 + 2400 = 2800
     $$
   - Plot the point (100, 2800) and draw a line through the points (0, 2400) and (100, 2800).

4. **Plot the revenue function $ R $:**
   - Start at the origin (0, 0).
   - Use the slope to find another point. For example, when $ n = 100 $:
     $$
     R = 6(100) = 600
     $$
   - Plot the point (100, 600) and draw a line through the points (0, 0) and (100, 600).

5. **Determine the number of baskets produced when costs equal revenue:**
   - Set the cost function equal to the revenue function:
     $$
     4n + 2400 = 6n
     $$
   - Solve for $ n $:
     $$
     2400 = 6n - 4n
     $$
     $$
     2400 = 2n
     $$
     $$
     n = \frac{2400}{2} = 1200
     $$

6. **Conclusion:**
   - The number of baskets produced when costs equal revenue is $ n = 1200 $.

By following these steps, you can sketch the graphs of the cost and revenue functions and determine that the number of baskets produced when costs equal revenue is 1200.

Knowee AI · Accepted Answer