Question

Jack is trying to determine how he can save money by cutting his electricity bill. He is currently on a standard use plan for electricity and pays 7.5 cents per kWh. He keeps track of when he uses electricity and is thinking about switching to an interval use plan for electricity which costs 3 cents per kWh for off-peak use and 15 cents per kWh for on-peak use. Off-peak hours are from 8PM - 8AM and on-peak hours are from 8AM - 8PM. Below is the chart of his electricity usage:

Jack’s Electricity Usage Per Month
1200 kWh between 8PM and 8AM
400 kWh between 8AM and 8PM

Explain and justify which plan would best suit his needs.

Answer 1

First compute his total monthly cost on each plan.

Standard plan (flat 7.5¢/kWh)
- Total usage = 1200 + 400 = 1600 kWh
- Cost = 1600 kWh × $0.075 = $120.00

Interval plan (3¢ off‑peak, 15¢ on‑peak)
- Off‑peak cost = 1200 kWh × $0.03 = $36.00
- On‑peak cost = 400 kWh × $0.15 = $60.00
- Total = $36 + $60 = $96.00

Comparison
- Interval plan costs $96 vs $120 on the standard plan, so he would save $24/month (20% of his current bill), or about $288/year.
- His weighted average cost on the interval plan = $96 / 1600 kWh = $0.06/kWh (6¢), which is below the 7.5¢ on the standard plan.

Break‑even rule (useful if his pattern changes)
- Let O be off‑peak kWh (1200) and P be on‑peak kWh. Interval is better when 0.03O + 0.15P ≤ 0.075(O + P).
- That simplifies to P ≤ 0.6·O. With O = 1200, the interval plan is better as long as P ≤ 720 kWh. His current P = 400 kWh, so he’s well within the safe range.

Recommendation
- Based on the usage you gave (1200 kWh off‑peak, 400 kWh on‑peak) the interval plan is the better choice: it saves $24/month (about $288/year) and yields a lower average rate (6¢/kWh).
- Caveat: this conclusion assumes there are no extra fixed charges, meter fees, or demand charges on the interval plan. If the interval plan has additional fees, or if his on‑peak use rises above ~720 kWh/month, the standard plan could become preferable.