Find the $\inf_{f\in M}\sup_{x\in[0,1]}$ of the given expression

Let $M$ be a set of continuous decreasing functions $f$ on the segment $[0,1]$ for which $f(1)=0$. Find the$$\inf_{f\in M}\left(\sup_{x\in[0,1]}\frac{xf(x)}{\int_0^1f(t)\,\mathrm dt}\right)$$

I will be grateful for any help!