Recall the dynamic program given by equation (8.6). Let f  min i∈N min wi≤q≤Q fq (i).

Consider the function defined as follows.

gq (i)  min wi≤q≤q

{fq (i) + fq−q+wi (i)},

for each i ∈ N and wi ≤ q ≤ Q. Now define g  mini∈N minwi≤q≤Q gq (i). Show that f  g.