For customers generating their own solar​ power, a certain power company charges them ​$3 per month per kilowatt​ (kW) of installed capacity and credits them ​$0.03 per​ kilowatt-hour (kWh) for excess electricity they export to the grid. A second power company charges customers a flat rate of ​$20 per month and credits them ​$0.04 per kWh for excess electricity they export to the grid. Determine the monthly bills for customers of both companies for each of the situations below.
​(a) Customer owns a 3​-kW system and exports 150 kWh monthly to the grid.
​(b) Customer owns a 5​-kW system and exports 240 kWh monthly to the grid.
Question content area bottom
Part 1
​(a) For the first​ situation, the monthly bill for a customer of the first company is ​$

enter your response here.

Let's break down the calculation for the monthly bill of the customer for both companies under the given situation (a).

### **First Company:**
- Charges: $3 per month per kilowatt (kW) of installed capacity
- Credit: $0.03 per kilowatt-hour (kWh) for excess electricity exported to the grid

For a customer who:
- Owns a 3-kW system
- Exports 150 kWh to the grid

**1. Cost for Installed Capacity:**
\[
\text{Cost} = 3 \, \text{kW} \times 3 \, \frac{\$}{\text{kW}} = 9 \, \$
\]

**2. Credit for Exported Electricity:**
\[
\text{Credit} = 150 \, \text{kWh} \times 0.03 \, \frac{\$}{\text{kWh}} = 4.50 \, \$
\]

**3. Monthly Bill:**
\[
\text{Monthly Bill} = \text{Cost} - \text{Credit} = 9 - 4.50 = 4.50 \, \$
\]

Thus, the monthly bill for a customer of the first company is **$4.50**.

### Do you have any questions on this? Would you like me to proceed with part (b) or the second company calculation for part (a)?

Here are 5 relative questions for you to consider:
1. What is the overall cost structure for larger systems?
2. How does exporting more kWh affect the final bill in both companies?
3. How would the bill change if the first company raised the per kWh credit?
4. What would happen if the system produced no excess electricity?
5. How does the flat rate model compare in terms of risk for customers?

**Tip:** Always check the break-even point to understand which company is more favorable in different usage scenarios.

For customers generating their own solar​ power, a certain power company charges them ​$3 per month per kilowatt​ (kW) of installed capacity and credits them ​$0.03 per​ kilowatt-hour (kWh) for excess electricity they export to the grid. A second power company charges customers a flat rate of ​$20 per month and credits them ​$0.04 per kWh for excess electricity they export to the grid. Determine the monthly bills for customers of both companies for each of the situations below. ​(a) Customer owns a 3​-kW system and exports 150 kWh monthly to the grid. ​(b) Customer owns a 5​-kW system and exports 240 kWh monthly to the grid.

Learn how to calculate monthly solar power bills for two companies. This problem covers key algebraic concepts such as cost per kilowatt of installed capacity and credits for excess kilowatt-hours exported to the grid. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation