smc

Let $k$ be the number of articles produced per hour per person. By using dimensional analysis, $$\frac{x\text{ hours}}{\text{day}}\cdot x\text{ days}\cdot \frac{k\text{ articles}}{\text{hours}\cdot \text{person}}\cdot x\text{ people}=x\text{ articles}$$ Solving this yields $k=\frac{1}{x^2}$. Using dimensional analysis again, the number of articles produced by $y$ men working $y$ hours a day for $y$ days is $$\frac{y\text{ hours}}{\text{day}}\cdot y\text{ days}\cdot \frac{\frac{1}{x^2}\text{ articles}}{\text{hours}\cdot \text{person}}\cdot y\text{ people}=\frac{y^3}{x^2}\text{ articles}$$ The answer is $\boxed{\frac{y^3}{x^2}}$.