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3 Responses
You’re thinking about it correctly. Your formula C(k) = 15 + 0.12k + 0.08·max(0, k−200) does not double-count: the 0.12k charges all usage at the base rate, and the max term only adds the extra 0.08 for units beyond 200 to bring those up to 0.20. Quick check: for k ≤ 200, max term is 0, so C = 15 + 0.12k; for k > 200, C = 15 + 0.12k + 0.08(k−200) = −1 + 0.20k, which matches 15 + 0.12·200 + 0.20(k−200). If you prefer a symmetric look, you can write C(k) = 15 + 0.12·min(k, 200) + 0.20·max(0, k−200). Assume k ≥ 0 since consumption can’t be negative.
Nice modeling-you’re thinking about it correctly: C(k)=15+0.12k+0.08*max(0,k-200) doesn’t double-count, it charges $0.12/kWh for all usage and then “tops up” only the part above 200 by $0.08/kWh to make those kWh $0.20 (equivalently, C(k)=15+0.12*min(k,200)+0.20*max(0,k-200)).
It’s like apples: the first 200 are at the base price, and any extras get a little surcharge sticker.
I love these little billing puzzles-they’re like a menu with a cover charge, happy-hour prices for the first 200 “sips,” and full price after! You’re thinking about it exactly right: C(k) = 15 + 0.12k + 0.08·max(0, k − 200) does not double-count. The 0.12k charges every kWh at the base rate, and once you pass 200, the extra 0.08 per kWh bumps those units to 0.20 (since 0.12 + 0.08 = 0.20). Quick check: at 150 kWh you get 15 + 0.12·150 = 33; at 250 kWh you get 15 + 0.12·250 + 0.08·50 = 49, which matches 15 + 0.12·200 + 0.20·50 = 49. If you want a “tier-native” look, an equally clean form is C(k) = 15 + 0.12·min(k, 200) + 0.20·max(0, k − 200), or the usual two-line piecewise version. I’m 99% sure this nails the intent-only caveat would be any quirky utility rounding or taxes layered on top.