Formula to sum item costs based on item library

Hi excel masterminds.

I have attached a sample workbook regarding my question.

I have a large spreadsheet consisting of 40 departments, all using the same items (all have ID's that are texts, in the sample WB they are named A-Z).
In Sheet 2, I have all the departsments, one column for each, listing their items used in a given timeframe.

I need a formula that can sum the item costs for the items used per department - with the item costs being determined by a list in another sheet.
In other words, I need a formula which checks the column for items (sheet 2), then looks up the 'item library' and sums the cost based on the item-cost values listed in the library (sheet 1).
There can be multiple items listed in one column and each listing needs to be included.

I know that I can create a "helper" column next to each department, with an INDEX-MATCH function to find the item cost, but I would prefer to avoid expanding the spreadsheet (simply due to it already being rather moderate in size).

Regards,
Fno

Paste into A13 and drag across:

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