SUM and IF formula based on background color

I have a spreadsheet that I need to sum numbers based on the background color of a cell. These numbers can be anywhere in the row. Here's an example of what i'm trying to sum. If I were to write this in english it would be:

For Cell A1 the formula would be "Sum the values of any cell that has a background color of yellow in the range of D1:I1."

For Cell B1 the formula would be "Sum the values of any cell that has a background color of orange in the range of D1:I1."

The spreadsheet is large with hundreds of rows and years of columns and the numbers with their colors move left and right all the time. The number values represent FTE (people required to do a task in a month) and the colors represent a particular phase of a project.

Thanks for your help.

Example