Rose bouquets: the first hour decides the fortnight
Roses fail in a particular way, and almost always for the same reason. The bud looks perfect, the petals are firm, and then the neck just below the head folds over and the flower hangs upside down while everything else in the vase carries on looking fresh.
That is an air lock, not old stock.
A cut stem draws water up a column of narrow vessels. Let air into that column, by leaving the stem out of water for too long or by cutting it dry, and the bubble sits there blocking the flow. The head is the furthest point from the cut and the first to be starved, so it is the first to give way. Water never reaches it again, and no amount of flower food will help.
What to do in the first hour
Unpack the box straight away rather than leaving it in the hall until the evening. Roses travel dry, and the clock on that air lock starts the moment they leave the water.
Recut every stem at an angle before it goes in the vase, taking off a couple of centimetres with a sharp knife. Secateurs and kitchen scissors crush the tissue instead of slicing it. If you can do the cut under running water or with the stem ends submerged, so much the better, because that keeps air out of the fresh wound entirely.
Then strip the leaves. Every leaf that would sit below the waterline has to come off, without exception. Submerged foliage rots within a day or two, the water goes cloudy and starts to smell, bacteria colonise the cut end and block it as effectively as any bubble. This single step does more for vase life than any sachet. Thorns can stay unless they are in your way, since scraping them off tears the skin of the stem and opens another route for bacteria.
Leave the leaves that stand above the water. They are working, and a stripped bare stem looks like a shop display rather than a bouquet.
The routine after that
Change the water every two days and rinse the vase properly while you are at it. Slime on the glass walls goes straight back into clean water within the hour. Washing the vessel matters about as much as refilling it.
Recut a centimetre off the stems each time, which takes a minute for the whole bunch and is often the difference between a week and a fortnight.
Keep the vase out of direct sun, away from radiators and away from the fruit bowl. Ripening fruit releases ethylene, which makes petals drop early.
If a head has already gone over
There is one trick worth trying, and it works occasionally rather than always. Cut the stem again, sharply and higher up, then lay the whole flower flat in a basin of cool water for an hour or two so the stem and head are both submerged. Sometimes the neck takes up water and stiffens again. If it does not, the head will not come back, and the honest move is to pull that stem out before it spoils the look of the rest.
Guard petals are a separate matter and cause a lot of unnecessary worry. The one or two coarse outer petals on each bud protected it in transit, they are meant to look slightly rough, and peeling them off reveals a clean bloom underneath.
Well kept rose bouquets hold for one to two weeks, which is the top of the range for fresh cut flowers. That figure assumes somebody is at home to take the box in. If the recipient in Sao Paulo is away for a few days, move the delivery date rather than leaving the flowers to wait in a hallway.