The Cherries chairman is welcoming ideas from the club's supporters as to how to lure more people through the turnstiles following disappointing gates so far this season.
Fans have aired their views and put forward numerous ideas via the Daily Echo's message boards in recent days, as the topic has been put under the microscope following Saturday's victory over Dagenham and Redbridge.
Eddie Howe's team continued their impressive form and entertaining play with a 3-0 win against the Daggers, which moved them up to third place in League One.
But despite Cherries' recent record and stylish brand of football, many have been left wondering why people in the town have not turned out in force.
Just 5,501 were in attendance for Saturday's success, while home fans accounted for 5,189 of a 5,949-strong gate against Peterborough, with a similar number going to last term's curtain-raiser against Rotherham despite it being in a lower division.
And in an attempt to increase numbers and revenue, Mitchell is keen to explore any ideas fans come up with.
When asked if he would look into initiatives such as letting children in for £1 when they attend with a paying adult, he said: I think we're constantly looking into different things.
We're constantly looking at ways to get more people in but we've got to be careful that we get the right thing for everybody.
It's a little bit of a balancing act to a degree, but we want to be able to help everybody to come to the football.
When asked if he would welcome ideas from supporters, he said: Yes, of course I would.
I'd like everybody's thoughts. We would pick the ones that will work. Some ideas are feasible and some aren't.
It's great to see people do recognise that the crowds we are getting are a little bit disappointing, and all suggestions of how we can get more people (are welcome).
I'm asking the floating supporters, directly, to come down to the club.
The team does deserve better attendances for the way they are playing and their commitment.
We're only two divisions off the Premier League and we're doing our bit especially the team. We want to be able to sustain it but we can only sustain it with income.
I'm sure people would be pleasantly surprised if they came down and it wouldn't take long before they got hooked and couldn't wait for the next Saturday to come.
It's a good experience and it's such a friendly experience. It's a great family day out.
Mitchell added: It is hard (financially) for lots of people but that includes the club as well.
We've just got to offer the best we can and keep pushing.
Mitchell revealed the club was looking into a promotion that involves discounts for key workers and members of the Armed Forces.