Choosing an Internet Plan with Variable Data Use
A family is comparing two monthly internet plans. Plan A costs $65.00 per month and includes 200 GB; extra data costs $1.50 per GB, charged per whole GB. Plan B costs $80.00 per month and includes 500 GB; extra data costs $0.50 per GB, charged per whole GB. A third plan, Plan C, costs $95.00 per month with no data cap. The family reviews six recent months of usage: 180 GB, 260 GB, 310 GB, 150 GB, 420 GB and 480 GB. They expect similar variation next year, including at least one month near 500 GB. They want the lowest expected annual cost but are worried about a single unusually heavy month. All prices include GST. A salesperson says Plan A is cheapest because its monthly fee is lowest.
1. Calculate the cost for each of the six months under Plan A and Plan B, and find the six-month totals.
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Plan A has 200 GB included, then $1.50 per extra GB. Costs: 180 GB -> $65.00; 260 GB -> 65 + 60 x 1.50 = $155.00; 310 GB -> 65 + 110 x 1.50 = $230.00; 150 GB -> $65.00; 420 GB -> 65 + 220 x 1.50 = $395.00; 480 GB -> 65 + 280 x 1.50 = $485.00. Plan A total = 65 + 155 + 230 + 65 + 395 + 485 = $1395.00.
Plan B has 500 GB included, so all six usages are at or below 500 GB. Each month costs $80.00. Plan B total = 6 x $80.00 = $480.00.
Plan C total = 6 x $95.00 = $570.00.
Over these six months Plan B is cheapest by a large margin. The salesperson's reasoning is wrong because the monthly fee is not the total cost when extra data charges apply.
2. Find the monthly usage at which Plan A and Plan B cost the same. Also find the usage above which Plan C becomes cheaper than Plan B.
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Between 200 GB and 500 GB: Plan A cost = 65 + 1.50(x - 200) = 1.50x - 235. Plan B cost = 80. Set equal: 1.50x - 235 = 80, so 1.50x = 315, x = 210 GB. At 210 GB both plans cost $80. Below 210 GB Plan A is cheaper; above 210 GB Plan B is cheaper, until other thresholds change.
For Plan C versus Plan B above 500 GB: Plan B cost = 80 + 0.50(x - 500) = 0.50x - 170. Plan C cost = 95. Set equal: 0.50x - 170 = 95, so 0.50x = 265, x = 530 GB. So Plan C becomes cheaper than Plan B only when usage is above 530 GB in a month. Below that, Plan B is cheaper.
3. Recommend a plan for the family. Use the six-month data and the break-even values, and state one risk in your recommendation.
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Plan B is the best recommendation from the data. Its six-month cost is $480.00, compared with $570.00 for Plan C and $1395.00 for Plan A. If the pattern repeats, the annual cost is about 2 x $480 = $960 for Plan B, versus $1140 for Plan C and $2790 for Plan A.
Plan B also has useful headroom: the highest observed usage is 480 GB, which is still inside the 500 GB allowance. The break-even with Plan C is 530 GB, so a single month near 500 GB does not make Plan C cheaper. Even a 600 GB month would cost 80 + 0.50 x 100 = $130 under Plan B, still below the $95 Plan C monthly fee only for that month, but the savings in other months keep Plan B cheaper overall.
The main risk is that the family's usage may rise above 530 GB often, for example with more streaming or remote work. In that case Plan C would become better. The family should monitor usage for a few months and review if several months exceed 530 GB.