Final answer:
To have ewe lambs reach puberty by the subsequent October following their birth for a breeding program, the latest breeding date should be in late March to early April, considering a gestation period of 150 days and an 8-month puberty onset period.
Step-by-step explanation:
The question pertains to the breeding management of sheep to ensure that ewe lambs reach puberty and are available for breeding the following fall season. Considering the gestation period of sheep is approximately 150 days, and it takes an average of eight months for lambs to reach puberty, the timing of breeding must be calculated to meet these constraints.
Starting from October 1st of the following year, counting back eight months for puberty and adding the gestation period of 150 days determines the latest possible breeding date. This calculation is crucial for the management of a breeding program seeking to optimize the availability of ewe lambs for the next breeding season.
With this in mind, the last possible date to breed the sheep would be roughly late March to early April, depending on the year's specifics, including if it's a leap year. This date ensures that the lambs are born latest by mid-September and will have reached puberty by the following October.