A factory produces 150 units of a certain product every day, but due to increased demand, they decide to operate for two extra hours each day, which results in a 25% increase in daily production. How many units are produced in total during a 30-day month with the increased production rate?
First, let's find out how many additional units are produced as a result of the 25% increase in daily production:

Additional Units = Original Daily Production * Percentage Increase
                 = 150 units * 0.25
                 = 37.5 units

Since it's not possible to produce a fraction of a unit, we'll round up to the nearest whole number:

Additional Units = 38 units

Now let's calculate the new daily production rate by adding the additional units to the original daily production:

New Daily Production = Original Daily Production + Additional Units
                     = 150 units + 38 units
                     = 188 units

Finally, we can find out how many units are produced in total during a 30-day month with the increased production rate:

Total Monthly Production = New Daily Production * Number of Days
                         = 188 units * 30 days
                         = 5640 units

So, the factory will produce a total of 5640 units during a 30-day month with the increased production rate.