How to create a row-by-row running total for a dynamic array?

Hello everyone,

I'm trying to create a single, dynamic formula that calculates a running total along each row. Each row's running total needs to start with a specific initial value from that same row.

Here is a simplified version of my data and the desired result.
Requirements table

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Relevant materials table

Desired solution

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I've tried several advanced array formulas but keep hitting roadblocks:

1. SCAN: This works perfectly for a single hardcoded row =SCAN(B2,J2:N2,LAMBDA(a,b,a+b))), but isn't dynamic.
2. BYROW: When I try to make it dynamic =BYROW(SCAN(B2,J2:N2,LAMBDA(a,b,a+b)))), it fails with a #CALC error because BYROW's LAMBDA expects a single value, but SCAN returns a whole array for each row so, nested arrays error.
3. MAKEARRAY: This feels like the right tool. My first attempt correctly looked up the data but didn't accumulate the total; it just added the starting inventory to each day's value individually.

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=LET( materials,A2:A5, startValues,B2:B5, relevantData,INDEX(J2:N8,XMATCH(A2:A5,I2:I8),XMATCH(C1:G1,J1:N1)), result,MAKEARRAY(ROWS(relevantData),COLUMNS(relevantData),LAMBDA(r,c,INDEX(startValues,r)+INDEX(relevantData,r,c))), result) 

My final attempt was to create a running sum inside the MAKEARRAY, but it failed with a #VALUE! error. I now understand this is because my syntax for creating the range to SUM was incorrect SUM(INDEX(relevantData,r,c):c).

I'd appreciate your help