There are currently 424 laying hens at Egg City Farm. Due to some considerations, the number of laying hens is decreasing at the rate of 15 hens per month. Currently the average number of eggs per hen is 1146 per month, and the production of eggs is increasing at the rate of 43 eggs per hen per month. Use the product rule to determine the rate at which egg production at Egg City Farm is currently changing per month.