Consider two treatments and a combination of them. Givennavailable experimental units, the problem is to determine the number of unitsn, to be assigned to the first treatment,n2to the second, andn, to the combination,n= Σi,ni,ni≥ 0,i= 1, 2, 3, subject to suitable optimality criteria. This study was motivated by an example of a weighing design withn= 18.n1= 2.n2= 9,ns= 7 given by Box and Tiao [2, Section 2.7.3]. The allocation seemed far from optimal leading to the present investigation.