Is it permissible to employ an elderly, less productive worker when there are more efficient workers available, especially if the manager has been authorized to appoint whomever he deems suitable, and dismissing this worker would make it difficult for him to find another job, while younger workers have been dismissed due to the availability of job opportunities for them?

Your authority to hire whomever you deem fit and dismiss whomever you wish does not permit you to appoint someone unsuitable for the job or to dismiss someone competent without justification. Rather, the obligation is to act solely in accordance with what serves the best interest and to appoint the most capable. You are an agent of the manager, and agency is founded upon trustworthiness. You are not permitted to act except in a manner that benefits your principal. Therefore, you are not allowed to dismiss competent individuals to employ less competent ones merely to show favoritism, unless the owner of the company explicitly authorizes you after the matter has been explained to him. The principal's permission is restricted by what serves the best interest, and any act involving favoritism that does not serve the company's interest is not permissible except with a clear directive from the company owner.