Profit from seed levels off when the bee populations are large enough to pollinate flowers as rapidly as they come into bloom.  However, the cost of adding large populations of bees eats into seed profits (purple lines). I assume that the cost of bees this season can be reduced by the number of offspring bees from the previous season, which is the same as the expected number of offspring this season. For each seed price, there are two sets of net profits. The purple curve with open symbols is for bees costing $40/gallon, where a gallon equals 10,000 bees, 3,500 of which are females. The purple curve with closed symbols is for bees costing $90 per gallon.

Note that there is a wide range of bee populations at which net profits (price for seed – cost of bees + savings from last year’s bees) don’t change much. This is particularly true when bees are inexpensive. The less one pays for bees, the less it eats into profits. There is little to lose by hedging one’s bets and putting out more than the optimum number of bees. If bees are expensive, it may be best to release fewer bees, because they eat into one’s profits rapidly the more one puts out. Although this reduces the rate of pollination, net profits may not suffer. The lower the price of seed, the fewer bees one should introduce into the field as well. Some growers increase their profits by rapidly pollinating their own fields and then renting bees to their neighbors for pollination. The income from bee rentals can significantly supplement the above profits for these lucky growers.