If it will please you To show us so much gentry and good will As to expend your time with us awhile For the supply and profit of our hope, Your visitation shall receive such thanks As fits a king’s remembrance.

erainbowd

Sum it all up with PROFIT.
The queen is gifted with political speech, able to use many words to make what is essentially a promise of money hidden in the veil of courteous language.
When I played the Queen, we cut most of this line, keeping only the thanks fitting a king’s remembrance. But reading it now, it expands Gertrude’s skill set considerably. She uses profit to suggest what she and Claudius will get out of them -profit more as a metaphor – but in using it to Rosencrantz and Guildenstern (to whom she’s promising king’s remembrance) she’s planting a seed for big bucks.
We don’t see politically adept women in the plays and I wouldn’t have credited her as such at first. But she’s good, this Gertrude, she’s a good political match for Claudius.