Display Minimum Value in Array

I'm wanting to create a formula to display the lowest value in an array with certain conditions and I can't wrap my head around the logic. The situation is I will receive prices on 3 items from 4 separate companies. Some companies may submit 3 prices or 2 prices or even 1 price that includes all 3 items in one number. If they submit only 1 price that includes different items a number is entered in one column and an asterisk is used to denote that items price is included in the other number in the row. I want a cell to return the lowest price or the lowest combination. I have attached a spreadsheet of this example so it will hopefully explain a little better.
example.xls

Hi
Please see sample solution attached.
Hope this helps
Good luck.
Tony

Thanks for the reply but I may have over simplified the example. The combination price may not include all items. For example abc door may be low on a combination of item 1 and 2 and then A-1 Door may be low on item 3. I hope this makes since otherwise I may need to modify my example sheet to be a little more complex.

Hi
If you are looking for the lowest combined price for the three lowest prices items try this example.
Good luck.
Tony

exampleREVISED.xls

Attached is a revised example that should more clearly show the complexity of what I'm trying for. Row 4 are the results that I am try to write a formula for. Also I'm not afraid of a little VBA if it is required.

Hi
Please find herewith my latest attempt. Because not all companies provide the same products it is difficult to provide a single solution. As such I have split the worksheet into three separate provider sections. Row 18 provides the solution for each provider sections and matches your required results.
Hope this helps.
Good luck.
Tony