Climate, soil quality, surrounding environment, sunlight, length of growing season, how much the 50 people use and what types of crops are all factors.
1 pound of harvested produce per day per person suggests 1 sqft per person per day. Round upwards to 400 sqft each for a year.
50 people equates to 20,000 square feet.
To account for pathways, increase that by 30%. If these 50 people will be picking their own produce, increase by 50%.
The weather is pretty screwy. Perhaps you won't get the desired conditions (too wet/dry hot/cold). increase the growing area to account for that as best you can.
Bugs can wail on crops despite your best effort. Increase your estimate by 25-50%
I once suffered from late blight that wiped out hundred of potato and tomato plants. Are the folks dependent on your production and if so, do they go without or look for another supplier?
If the soil is poor, and production is low, increase the estimate accordingly.
Crop selection has it's place. Brussels sprouts will take longer to raise than lettuce. Do you skip the sprouts to raise faster crops such as turnip or yellow squash?
Is there time in the season to raise some slow crops and fill in the early spring and late fall with fast and tasty
greens?
There will be blemished and misshapen produce. The people may not accept them, but it may be possible to turn ugly tomatoes into sauce, ugly cukes into pickles.
Providing vegetables for 50 people on an acre is a challenge. 25/acres can work with the right conditions, skillful attention and fair weather. 10/acre may be more realistic.
Does this growing space account for space needed for support?
I use heaps of grass and leaves. An acre of grass and an acre of woods sure is a handy thing to harvest for mulch and
compost.
Have you accounted for parking? If these 50 people are coming to the farm to pick up the produce, they'll need a few parking spots nearby.
A toolshed, farmstand or other structure won't take up much room but needs to be figured in. It's not just the footprint of the building, but the shade behind and walkway to it it that can be lost.
The best answer I can come up with is 1-5 acres.