Question

how might the use of herbicides on a farm affect the honey production of a local bee keeper?

Answer 1

Herbicides are  used to kill unwanted plants from the feild. This includes the wild flowers growing in the field margins. As a result there are far fewer flowers for the bees . 
It is a fact that bees kept in a city generally do far better and make more honey than bees kept in rural locations because city bees have access to parks and people's gardens with their wide range of flowers, whereas rural bees are now faced with agricultural monocrops and far fewer wild flowers.

Answer 2

This is because the herbicides will kill all the herbs which are harmful for the farm but beneficial fro bee keepers,because bee dwell on herbs and feed on their flowers if they will be killed then bees will not get sufficient food or juice of flowers,they have to go far to bring the nectar so they will leave the hive near that particular field where the herbicides are used.