Choosing the Cheaper Electricity Plan
A household receives two electricity offers and must decide which suits its usage. Plan A charges a fixed supply charge of $0.95 per day plus 28 cents per kWh used. Plan B has no supply charge but charges 34 cents per kWh, and adds a $15 per quarter account fee. The household's quarterly usage is not constant: last summer quarter it used 1450 kWh, the autumn quarter 980 kWh, the winter quarter 1120 kWh, and the spring quarter 760 kWh. The billing quarters are 91, 92, 90 and 92 days respectively. The household currently budgets $420 per quarter for electricity and is considering installing a solar system that would cut usage by about 30% in every quarter.
1. Calculate the annual cost under each plan using the four quarters of usage, and state which plan is cheaper overall.
Read the worked answer
Plan A: supply charge = 0.95 × (91+92+90+92) = 0.95 × 365 = $346.75. Usage charge = 0.28 × (1450+980+1120+760) = 0.28 × 4310 = $1206.80. Total = $1553.55.
Plan B: usage = 0.34 × 4310 = $1465.40. Account fees = 15 × 4 = $60. Total = $1525.40.
Plan B is cheaper by $1553.55 − $1525.40 = $28.15 per year. Note the margin is small, so a change in usage could reverse it - this is the judgement the question is testing, not just the arithmetic.
2. The household expects the 30% solar reduction. Recalculate both plans and explain whether the cheaper plan changes.
Read the worked answer
New annual usage = 4310 × 0.70 = 3017 kWh.
Plan A: supply stays $346.75 (fixed regardless of usage). Usage = 0.28 × 3017 = $844.76. Total = $1191.51.
Plan B: usage = 0.34 × 3017 = $1025.78, plus $60 fees = $1085.78.
Plan B remains cheaper, now by $105.73. The gap widens because Plan B's higher per-kWh rate is applied to a smaller quantity, while Plan A's fixed charge is unchanged. The reasoning point: fixed charges dominate when usage falls, so a plan with low fixed cost benefits more from reduced usage.
3. The household wants to keep quarterly bills at or below $420. Identify which quarters breach the budget under the plan that is cheaper annually, and comment on whether the annual comparison is sufficient for budgeting.
Read the worked answer
Under Plan B (cheaper annually), quarterly cost = 0.34 × kWh + $15.
Summer: 0.34 × 1450 + 15 = 493 + 15 = $508 → breaches by $88. Autumn: 0.34 × 980 + 15 = 333.20 + 15 = $348.20 → within budget. Winter: 0.34 × 1120 + 15 = 380.80 + 15 = $395.80 → within budget. Spring: 0.34 × 760 + 15 = 258.40 + 15 = $273.40 → within budget.
Only summer breaches. The annual total for Plan B is $1525.40, which averages $381.35 per quarter - under $420 - yet one actual quarter exceeds the budget. So the annual average hides a seasonal spike. A sound answer notes that budgeting must be done quarter by quarter, and the household could smooth this by setting aside the surplus from cheaper quarters or by comparing Plan A's summer bill ($346.75 + 0.28×1450 = $752.75) - which is even worse in summer - confirming Plan B is still the better choice despite the breach.