The first thing they'd do is look for subsidies and tax breaks, taking a lesson from the free market farmers. For the launching facility they would have received tax breaks and subsidies from the local area. Same as for building the rocket and lander. The US government would have a "National Prestige Strategic Subsidy", funding projects which enhanced the US in the view of the world. It would be created to help companies who were spending their own money for the glory of the US, thereby saving tax money. Endless press reports would point out the private enterprise aspect of this venture. Just turn the capitalists loose.

Even before the attempt, they would have sold the name. "Mars" would have become "Monsanto". Then it would have sold the launcher name, the lander name. It would have had the official beer, the official scotch, the official PC, the official tablet. And so on. The sides of the rocket would be painted with the logos of larger companies, such as Nike, GoDaddy, Xerox, Coca Cola.

After landing pictures of the landscape, analyses of the minerals, all that stuff would be bundled and sold to the highest bidders. Anyone writing about the possibility of life on Monsanto would be sued, as "Monsanto" would be copyrighted, trademarked.
It would have sold the seats for the launch, the TV rights for the launch, the TV rights for interviews with the people on the lander while on the journey.

A truly resourceful entrepreneur could come up with more ideas. After all, that's the genius of free market capitalism.