The continuous mixing set is S={(s,r,z)∈ℜ×ℜn+×Zn: s+rj+wjzj≥fj,j=1,…,n} where w1,…,wn>0 and f1,…,fn∈ ℜ. Let m=∣{w1,…,wn}∣. We show that when w1∣…∣wn, optimization over S can be performed in time O(nm+1), and in time O(n log n) when w1=…=wn=1.