To be precise, the make at home version is probably higher than the manufacturing cost (not including packaging and distribution to markets). But the price of the ingredients is much less than any store bought product, even generic versions.
The article compares 50 cents per tablet for the name brand in the store to 2.5 cents for the made at home version.
By Grabthar’s Arm and Hammer, what a savings.
Aspirin is not included, but generic pills are cheap. I imagine you could crush one or two pills into the seltzer mix if you wanted.
Quoting a “Make Aspirin If You’re Lost in the Woods” page at WikiHow:
Steep it as you would tea for 1/2 hour. This is basically aspirin - the chemical that aspirin is made of is found in the bark of willow trees.
The article gives several warnings. One warning is to select trees far enough from the road to be clean to avoid getting sick and that the salicylic acid in willow bark is more irritating than the acetylsalicylic acid in regular aspirin. Perhaps you should read the entire article.
Making aspirin is also a common chemistry assignment. See an example at About.Com’s “How to Make Aspirin - Acetylsalicylic Acid” page.