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How do I calculate the total amount per category by multiplying amounts with distinct multipliers? [closed]

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I know how to program in python/go/bash, but I'm a super noob when it comes to excel or google sheets. Sometimes they are super helpful, but I often find it difficult to figure out what's an easy approach to solve problems.

My issue here is mostly not knowing what query to search for / how to describe my problem.

In this case, I'm trying to calculate what length of various cables I need to buy to rewire my house (coax, cat6a, etc): left axis is cable conduits, multiplier is conduit length, and top axis is cable types. This issue applies to a lot of other things I've had to deal with in the past too so I'll generalize below.

Here is an example table for the initial data/planning:

multiplierabcd
11021
22011
3301
44012

What I want to achieve is:

xntotal
a3=2*10+1*30
b2=1*20+1*40
c3=1*10+2*40
d1=1*20

I know that transposing from c1:f1 is my first step to creating the left axis, and I have experience using SUMIF, but this is more complex as it needs multiplication.

Bonus: I would also love to be able to generate this table

x-ncountlen
a-1210
a-3130
b-2120
b-4140
c-1110
c-4240
d-2120

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