Examkin

Question

Difficulty: MediumWeighted Averages in Applied Contexts

An electric utility provider generates energy from three distinct sources: Solar, Wind, and Natural Gas. Solar power accounts for 20%20\% of total production at a generation cost of $40\$40 per megawatt-hour (MWh). Wind power accounts for 40%40\% of total production at a generation cost of $30\$30 per MWh. Natural Gas accounts for the remaining production at a generation cost of $80\$80 per MWh. What is the weighted average cost, in dollars per MWh, of the electricity generated by the utility provider?

  1. A
    $44\$44
  2. B
    $48\$48
  3. C
    $50\$50
  4. $52\$52Answer
  5. E
    $56\$56

Answer

The weighted average cost of electricity is $52\$52 per MWh.
The correct answer reflects the sum of each energy source's unit cost multiplied by its proportion of total output: Solar (0.20×$40=$80.20 \times \$40 = \$8), Wind (0.40×$30=$120.40 \times \$30 = \$12), and Natural Gas (0.40×$80=$320.40 \times \$80 = \$32). Adding these components yields $8+$12+$32=$52\$8 + \$12 + \$32 = \$52 per MWh.

Step-by-Step Solution

1
Determine the percentage weight of each energy source.
Solar =20%=0.20= 20\% = 0.20, Wind =40%=0.40= 40\% = 0.40, Natural Gas =100%−(20%+40%)=40%=0.40= 100\% - (20\% + 40\%) = 40\% = 0.40.
The total proportion of all energy sources must sum to 100%100\% (1.001.00).
2
Calculate the weighted cost contribution for each energy source.
Solar: 0.20×$40=$80.20 \times \$40 = \$8. Wind: 0.40×$30=$120.40 \times \$30 = \$12. Natural Gas: 0.40×$80=$320.40 \times \$80 = \$32.
Multiplying individual unit costs by their corresponding weights yields their contribution to the total average cost per unit.
3
Sum the weighted contributions to find the overall weighted average cost.
Weighted Average Cost =$8+$12+$32=$52= \$8 + \$12 + \$32 = \$52 per MWh.
Adding the individual component contributions yields the overall weighted average.

Key Concept

Weighted Average Formula: Weighted Average=∑(wi×xi)\text{Weighted Average} = \sum (w_i \times x_i) where wiw_i represents the relative weight (fraction or percentage) of each component xix_i, and ∑wi=1\sum w_i = 1.
Estimated Time:1m 30s
Rate this question

Topics

Weighted Averages in Applied Contexts

More questions from this topic