if $x_i,y_i,c_i,d_i$ all are  monotonically decreasing sequences,
$$\max_i \frac{x_i}{c_i}>\max_i \frac{y_i}{c_i}$$
then $$max_i\frac{x_i}{d_i}>\max_i \frac{y_i}{d_i}$$
can be derived？