Tire Pressure/contact Patch

I JUST PURCHASED A SET OF 16X7.5 850 WHEELS WITH 235/50-16 CONTISPORT CONTACT TIRES. THESE ARE AN UPGRADE FOR MY '89
735i. I KNOW THAT TIRE CONTACT PATCH IS = TO WEIGHT AT CORNER /TIRE PRESSURE. SINCE THESE TIRES HAVE A WITH OF 8.7", WHAT WOULD BE THE OPTIMUM TIRE PRESSURE TO GIVE THE OPTIMUM CONTACT PATCH?

From your equation it follows that you get the largest contact patch with a flat tire, but that's not the same as "optimum". Maybe one of those tire and wheel outfits can help, like:
http://www.tirerack.com/tires/index.jsp

Enter "tires" into www.google.com and you'll get lots of sites to try. You could email your question to them, and please post what you find out.