We let x and y represent the number of Outfits A and B, respectively. Such that the number of zipper that each will use are 2x and y, respectively. The number of designer buttons that each will require can also be expressed as 5x and 8y, respectively. The mathematical equations that would best represent the scenario are,
2x + y = 171
5x + 8y = 576
The values of x and y are 72 and 27, respectively. Thus, the company will be able to make 72 outfit A and 27 of outfit B.