The Western Dallas Milk Company is producing milk at the rate of $5000$ gallons per hour. The company$$s clients request $50,000$ gallons of milk over the course of the day. This demand is spread out uniformly from $8\mathrm{.}00$ am to $1\mathrm{.}00$ pm$.$ If there is no milk available, clients will wait until enough is produced to satisfy their requests.

The company starts producing at $8\mathrm{.}00$ am with $15,000$ gallons in finished goods inventory. At the end of the day, after all the demand is met, the plant keeps producing until finished goods inventory has been restored to $15,000$ gallons.

At what time during the day will the clients start waiting for their requests to be filled?