Lookup/Index type formula to Calculate Marginal Expense

Dear forum,
I'm afriad I am not grasping the formulas as quickly as I would like. I am having problems deciding whether I should be using a lookup or index type formula and whether I should be breaking the table into different parts to get the desired results. Probably in the right hands, it could be accomplished with either and other. However I have watched a few related videos and am still stuck. Any insigh or solutions would be greatly appreciated.
I want to calculate employee mileage expenses. Please see the attached file for clarification.
The dollar value is calculated based on (a) the size of the car engine, (3 size catogories, 0-1200cc, 1201-1500cc and 1500cc+) and (b) the ammount of miles. The expense per mile is different for the first 6437 miles than miles over 6437. (As shown in cells A5:D7). The desire is enter the mileage in cell B12, select the engine size in cell B13 and the a formula in B14 would calculate the actual expense.
So, to clarify, I'm looking for a formula for cell B14, or advise on restructing if required.
Thank you again for any insight.

There are a few approaches to incremental processes like this - a quick approach given your setup...

First revise boundaries such that the values equate to the last unit of the prior rate, ie:

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Then create incremental change rates for each rate in your table (ie the movement from prior rate to current)

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Then result can be calculated using:

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the above for 12k miles for 1201-1500c would generate 429,109.31

edit: should add, if you really have only two tiers to deal with then a basic SUM construct would suffice - again where A6 is 0 and A7 is 6437

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the SUMPRODUCT route is more useful where there are many tiers.