I guess if my weekly food budget was only $40 then I would also think that $40 for breakfast foods and snacks for 4 days was too much to pay. However, I cannot imagine feeding a family of 2 on so little when the maximum monthly allotment for food stamps is $367 for the same size family.
I regularly keep my monthly budget in the $160 neighborhood, so $40 a week. I admit it's just me and DD10, though, and I am not having to feed an ever-hungry teenage boy

And the $40 is straight food, it does not include paper products, toiletries, etc. because I buy those separately at different places.
It's not an accident I get our grocery bill down this low, but it doesn't take a huge effort either. I pull it off by grocery shopping only once every two weeks, ALWAYS having a meal plan and shopping from a list, buying store brands, not buying a lot of prepared foods (some, but very little compared to other families) or lots of other junk. If we want a treat like cookies, I generally make it from scratch, but only on weekend because I am a working single mother. I watch for sales on meat and stock up for a month or two when the prices are good and am "aware" of prices in general so I know when something is a good deal and when it's not. I don't go heavy on meat servings - I keep it to about 4 oz each at a meal, but that's actually a proper serving size. We fill up on veggies - those I buy in season or frozen but my grocery bill is still usually half fruits/veggies. We don't eat a lot of expensive meat cuts - we eat a lot of chicken, some ground beef, ham, pork chops, etc. - but we don't eat the crud cuts either, and I do have a soft spot for NY strip steaks once a month or so. We have meatless dinners about once or twice a week not really to cut costs but because I am a bean and cheese freak and love meals based on those. I buy all my bread products at a bakery store. I don't coupon maddly, although I usually have one or two for each grocery trip (stores in our area do not double).
One thing I've found that makes a HUGE difference in addition to everything above is where I shop. I found a warehouse-style market (regular size products but the shelves are basic and things are stocked in their cardboard boxes) that runs 20-30% less on average than the typical supermarkets in our area. I have to drive 7 miles each way to get there, and it caters heavily to the Hispanic market so many of the products I buy are labeled half in English and half in Spanish, but they are the same products as the companies sell otherwise so they suit me just fine. The store is not a Kroger, but is owned by the same parent company so all of store brands are all Kroger (it's called FoodsCo). The brand selection isn't as huge as the supermarkets in my area, and every now and then there's something I want that they just don't carry, but they have 98% of what I need.
So, yes, it can be done. But if I shopped at more expensive places, didn't buy in season, didn't pay attention to meat sales, etc. I can imagine easily spending much more and coming closer to the food stamps number - I just think I have better things to do with my money so I don't!