A technology consultant is analyzing server costs. A cloud provider charges $100 for 10 TB storage initially, and each additional TB costs $8. However, a competitor charges $180 for 20 TB, and $5 per additional TB beyond 20. After how many months will the total cost of the second provider exceed the first, assuming storage usage grows by 2 TB each month starting from 10 TB? - Treasure Valley Movers

A Technology Consultant is Analyzing Server Costs. When Will Competitor Pricing Surpass Initial Plans?

As data demands surge and cloud infrastructure shapes modern business strategy, cost modeling has become a critical skill for technology consultants. The current landscape shows a growing focus on predicting infrastructure expenses as storage needs expand. A common scenario involves comparing two cloud storage solutions: one starts strong with a flat $100 fee for 10 TB, plus $8 per extra TB, while a competitor offers 20 TB upfront for $180, with $5 charged per additional TB beyond that. Compounding this dynamic is the reality that many organizations begin their cloud journey at 10 TB and increase usage by 2 TB each month. With operational efficiency on the line, understanding when one pricing model overtakes another is essential knowledge.

Why A Technology Consultant is Analyzing Server Costs
A technology consultant is analyzing server costs. A cloud provider charges $100 for 10 TB storage initially, with each extra TB costing $8. Meanwhile, a competitor offers a 20 TB base plan at $180 and $5 per additional TB beyond that. As infrastructure scaling becomes a common operational priority—driven by remote work, AI workloads, and expanding digital services—consultants are tasked with forecasting long-term expenses. The challenge intensifies when usage grows by 2 TB monthly, requiring precise modeling to anticipate cost inflection points.

An Example: When Does the Competitor Exceed the Initial Plan?
How a technology consultant is analyzing server costs: The first provider’s total cost after n months depends on usage growth—starting at 10 TB and rising by 2 TB each month. With the initial 10 TB priced at $100 and $8 per additional TB, usage over n months amounts to 10 + 2*n TB. Beyond 20 TB, the margin spikes to $5 per extra TB.
The competitor’s cost: $180 for the base 20 TB, plus $5 for any amount over 20 TB.
Setting up the split model:

• Storage after n months: s(n) = 10 + 2n TB
• Cost from provider A:
    If 10 + 2n ≤ 20 → $100 + 8 × (2n)
    If 10 + 2n > 20 → $100 + 8×10 + 5×(2n − 10)
• Cost from competitor:
    If *