Scoring based on conditional formatting

I have a spreadsheet that containing 6 categories (in columns). Each category has 9 scenarios (in rows) with the top row detailing the best scenario / outcome in each of the categories (and a rating of 9 applied) and the 9th row detailing the worst scenario / outcome for each of the categories (and a rating of 1 applied).

I am wanting the user to select the most appropriate scenario in each of the categories by highlighting the cell in a colour (say yellow). Once completed each category / column would have one coloured cell. In the 7th column I would like to have a score for each row based on the highlighted cell. Totalled up this would provide a total score or rating.

For example if the responses for 2 categories were highlighted in row 9 (resulting in a score of 2), 2 categories highlighted in row 6 (resulting in a score of 12) and two in row 9 (resulting in a score of 18) the total score would be 36.

Is the above possible and is this the best approach. I am limited by the number of columns available and have 2 spare columns if needed to apply formulas etc.

Regards
FBS