Dave,
This is like a constrained menu-based choice, which you could indeed just program up in Lighthouse Studio as a free-format CBC question (allowing multi-check response, and with some fancy Javascript verification on each question, to force the respondent to spend exactly 10 dollars or no more than 10 dollars on the alternatives).
Then, you could conduct the modeling and analysis using our CBC/HB software (which you have a license to, if you have a license to our CBC system within Lighthouse Studio).
So, you have two attributes: brand & price. You would allow multi-checks in the CBC task. And, you would need to reformat the data in a special way for CBC/HB analysis (not hard, as you can do this in Excel and create .CSV file to submit to CBC/HB). If you constrained the respondent to spend exactly 10 dollars, then you'd just model it up as brand effects plus price effects. But, if you allowed respondents to spend less than 10 dollars, then you'd use the "synthetic None" approach of assigning any slack in demand to the None alternative. The respondent wouldn't see the None alternative in the questionnaire...but we'd model the data with a None option as if the respondent had seen it.