INDEX/MATCH Excel Question

Hello all and thanks in advance for the help. I'm trying to create a formula that will find the minimum cost of a tube size, given the finished part OD and ID (OD of the tube to make a part must be greater than or equal to the part OD and the ID the opposite). I've simplified the equation I have so far for this example, but ignore the IF(LEFT) portion of the formula for now. I have two sheets, the second is named 'Tube Prices'. Below is what they look like respectively:

Material Tube Cost Part ID Part OD
F0001 300 4.5 5

Material Tube ID Tube OD Price
F0001 4.25 5 $300.00
F0001 4.25 5 $400.00
F0001 4.25 5 $200.00
F0001 5 5.75 $100.00
F0001 6 7 $350.00


And here is the equation I'm using:

=IFERROR(IF(LEFT(A2,1)="F",INDEX('Tube Prices'!$A$2:$D$6,MATCH(1,('Tube Prices'!$A$2:$A$6=A2)*('Tube Prices'!$B$2:$B$6<=C2)*('Tube Prices'!$C$2:$C$6>=D2),0),4),0),)

Currently it's returning the first match, but I'd like to get it to return the cheapest price in that size (200). I need to keep the sheets set up as they currently are FYI, and I've had no luck with the min() function in that formula. Let me know any suggestions.

Hi
Use in B2

Formula:

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