A company has three divisions. To estimate the total amounts of the company’s accounts receivable, random samples of these accounts were taken for each of the three divisions, yielding the results shown in the following table:

Division 1 Division 2 Division 3 Ni 120 150 180 ni 40 45 50 xi $237 $198 $131 si $93 $64 $47 If a total sample of 135 accounts receivable is to be taken, determine how many of these should be from Division 1 under each of the following schemes.

a. Proportional allocation

b. Optimum allocation, assuming the stratum population standard deviations are the same as the corresponding sample values