Create Pie Chart From Table Summary Results

Attached is five months of dummy sales data for eight products. My objective is to filter this data with date ranges (using Column A in Data sheet), and have the corresponding pie slices (shown in Pie Chart Sheet) be the summation of the Products grouped by their designated letter. Currently, the result I am getting is 6 pie slices for "Product A" and this is wrong. I want to see "Product A" show up only once in the LEGEND and only as one aggregated pie slice. The same holds true for the rest of the Product Letters.

I want to avoid using Pivot Tables. My objective is to keep my layout clean and simple. I would like to know if anyone out there could help me figure out a formula that will automatically catagorize all of the resulting filtered data by the Product Letter they share. Once the formula categorizes or groups together all of the resulting filtered data by Product Letter, I would like the formula to calculate a summation for each Product Letter category. After the formula finishes the summation task I would like the formula to feed these results to a Pie Chart. The resulting chart I would like to see will show individual pie slices for each Product Letter resulting from the date range filtering operation performed on Column A. The resulting letters can be anywhere from "A" to "H". My goal is to only have one individual pie slice representing each of the Product Letters resulting from a Date range filter. I thought such a task would be as easy as baking a pie, but it's turned out to be beyond my Excel skills.