/sci/ - Science & Math

Let's denote [math]S[/math] as a set of continuous monotonically decreasing functions [math]f: \mathbb{R} \rightarrow [0, 1] \subset\mathbb{R}[/math], for which [math]f(1) = 0[/math]. Find [math]\inf_{f\in S}\sup_{x\in[0,1]\subset \mathbb{R}}\frac{xf(x)}{\int_{0}^{1}f(t)dt}[/math].

Tips to approach this?