Question

A beekeeper lives adjacent to an apple orchard. The orchardowner benefits from the bees because each hive pollinates about one acre of apple trees. The orchard owner pays nothing for this​ service, however, because the bees come to the orchard

without his having to do anything. Because there are not enough bees to pollinate the entire​ orchard, the orchard owner must
complete the pollination by artificial​ means, at a cost of ​$1010 per acre of trees. Beekeeping has a marginal cost MC=10+5Q​, where Q is the number of beehives. Each hive yields ​$5050 worth of honey. How many beehives will the beekeeper​ maintain?

Answer 1

The beekeeper will maintain 1008 beehives to maximize their profit.

Step-by-step explanation:

To determine the number of beehives the beekeeper will maintain, we need to compare the marginal cost of maintaining each hive to the benefit of honey produced by each hive. The marginal cost (MC) is given as MC = 10 + 5Q, where Q is the number of beehives. Each hive yields $5050 worth of honey. The beekeeper should maintain the number of beehives at which the marginal cost of maintaining an additional hive is equal to the benefit of honey produced by that hive. Therefore, we can equate the marginal cost to the benefit as follows:

10 + 5Q = 5050

Simplifying the equation, we get:

5Q = 5040

Dividing both sides by 5, we find:

Q = 1008

Therefore, the beekeeper will maintain 1008 beehives.