Concerning cost/benefit of feeding, this popped up right away:

> In an attempt to determine the effect of feeding on Apis mellifera L. populations and the economic value of feeding colonies for spring production of package-bees, a feeding experiment was conducted to evaluate the effect of feeding time and feeding treatments on the A. mellifera population, and to compare the cost with the benefit of feeding. Colonies produced significantly more bees from fall feeding than from spring feeding or continuous feeding from fall to spring. 

> Colonies fed with protein supplement containing 21% protein from Torula yeast and/or syrup also produced significantly more bees than unfed control colonies. Colonies fed with ⅓ the amount of protein supplement in the fall had the potential to yield high adult bee populations and a net gain in production of package-bees. Feeding sugar syrup in spring was less profitable than feeding protein supplement in fall.

Effect of Supplemental Feeding of Honeybee (Hymenoptera: Apidae) Populations and the Economic Value of Supplemental Feeding for Production of Package-Bees. Ying-Shin Peng  Jerry M. Marston  Osman Kaftanoglu. Journal of Economic Entomology, Volume 77, Issue 3, 1 June 1984, Pages 632–636, https://doi.org/10.1093/jee/77.3.632

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