FO OF B737 RPTS THAT COMPANY PRESSURED FLT CREW TO FLY AT FL350 WITH AIR CONDITIONING PACK WRITE-UPS AND MEL ITEMS ON BOTH PACKS. TWICE DURING THE SUBSEQUENT FLT; BOTH PACKS WERE SIMULTANEOUSLY INOP.

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ACFT ALREADY HAD MEL 21-6A; WHICH RESTR THE USE OF THE L PACK. ON PREFLT; WE DISCOVERED THE HIGH MODE OF THE R PACK WAS INOP. MEL 21-2C WAS ADDED; WHICH INCLUDES AN OPS NOTE IN 2 DIFFERENT PLACES OF THE MEL (ONE AT THE BEGINNING; REPEATED AGAIN AT THE END) TO ADHERE TO THE RESTRS OF MEL 21-1 FOR SINGLE PACK OP. FROM A SYS SENSE; THIS MAKES SENSE BECAUSE IF THE L PACK FAILED INFLT; THE R PACK WOULD TRY TO GO TO THE HIGH MODE; WHICH WAS INOP; SO WE WOULD GO FROM 2 PACKS TO NO PACKS ALL AT ONCE. THE CAPT EXPLAINED THIS ALONG WITH HIS DESIRE TO FLY AT FL250 INSTEAD OF FL350 TO DISPATCH; MAINT CTL; AND THE FLIGHT OPS AGENT; OUR FMS SHOWED THIS WOULD TAKE AN ADDITIONAL 700 LBS OF FUEL; WHICH WE ALREADY HAD ON BOARD. DISPATCH SAID IT WOULD TAKE OVER 2000 LBS EXTRA TO GO AT FL240; POSSIBLY BECAUSE THEY PLUGGED IN .74 MACH OR SOME OTHER SPD THAN ECONOMY; WHICH THE FMS USES. MAINT CTL CLAIMED THE OPS NOTE DID NOT APPLY BECAUSE THE PACK WORKED FINE IN AUTO -- IT WAS JUST THE HIGH MODE THAT WAS INOP. THE CAPT SUGGESTED OPERATING AT FL250 OR BELOW BECAUSE THAT WAS THE SAFEST SOLUTION TO THE CONFUSION; BUT EVERYONE DISAGREED BECAUSE OF THE EXTRA 700 LBS OF FUEL. THE FLIGHT OPS AGENT AGREED TO FOLLOW UP TO TRY TO CLARIFY THE MEL. THE CAPT AGREED TO OPERATE AT FL350 BECAUSE THE FLIGHT OPS AGENT SUPPORTED GOING TO FL350. WE TOOK OFF WITH THE L PACK OFF PER MEL 21-6A AND THE R PACK IN AUTO. AS SOON AS WE WERE AIRBORNE; THE AIRFLOW FROM THE R PACK SHUT OFF AS IT TRIED TO AUTOMATICALLY GO INTO THE HIGH MODE; WHICH IT IS DESIGNED TO DO; BUT THE HIGH MODE WAS INOP. AFTER FLAP RETRACTION; WE TURNED THE L PACK ON PER MEL 21-6A AND THE AIRFLOW FROM BOTH PACKS WAS RESTORED. DURING THE APCH INTO PORTLAND; WE TURNED OFF THE LEFT PACK PER MEL 21-6A; AND ONCE AGAIN THE R PACK IMMEDIATELY SHUT DOWN AS WELL.