Of course not. E.g., let 

- $(x_1,x_2,x_3,,x_4,\dots)=(3,1,1,1\dots)$;
- $(y_1,y_2,y_3,y_4,\dots)=(2,2,2,2\dots)$;
- $(c_1,c_2,c_3,c_4,\dots)=(1,1,1,1,\dots)$;
- $(d_1,d_2,d_3,d_4,\dots)=(3,1,1,1,\dots)$.

Then $\max_i\dfrac{x_i}{c_i}=3>2=\max_i\dfrac{y_i}{c_i}$ but $\max_i\dfrac{x_i}{d_i}=1<2=\max_i\dfrac{y_i}{d_i}$.