LAMBDA + LET — Tax Bracket Engine via MIN/MAX Clamps

You're a tax analyst computing progressive tax owed for 10 taxpayers. Columns A–B contain TaxpayerID and Income.

The bracket schedule (3 brackets):

The classic implementation is a 3-deep nested IF — but MIN/MAX clamps handle it more cleanly: each bracket contributes amount_in_bracket × rate, computed once per bracket using MIN/MAX to extract the income within each band. Because the brackets are independent, you can sum them with no branching at all.

Your task:

1. Define a single-input LAMBDA(taxableIncome, …) whose body uses LET to bind three intermediate tax amounts bracket1Tax, bracket2Tax, bracket3Tax (one per bracket), then returns their sum. Invoke the LAMBDA inline on each row. (Names like b1/b2/b3 would visually shadow A1-style cell refs in column B, so spell the role out.)
2. The clamps:
   • bracket1Tax = MIN(taxableIncome, 10000) × 0.10
   • bracket2Tax = MIN(MAX(taxableIncome − 10000, 0), 30000) × 0.20 — the 30000 is bracket-2's width (40000 − 10000)
   • bracket3Tax = MAX(taxableIncome − 40000, 0) × 0.30
3. Drag-fill from C2 → C11.

Graded cells: C2 (T-001 5000 → 500), C7 (T-006 45000 → 8500), C11 (T-010 150000 → 40000).