Transportation Secretary Elizabeth Hanford Dole appointed an 11-member commission yesterday to study how to end federal management of the Amtrak passenger rail system.

"In an era of large deficits, limited budgets and other, more pressing national needs, it's time we found a way to both relieve the federal taxpayer and preserve viable rail passenger service in this country," Dole said in a statement.

The administration has long urged sale of Amtrak, but all efforts to end funding for the system have been rejected by Congress. In its fiscal 1988 budget request, the White House proposed selling Amtrak's northeast corridor for $1 billion, but it has no buyer in mind.

Calling Amtrak a "long-term drain on the federal treasury" that has cost taxpayers $12.4 billion since the government created it in 1970, Dole assigned the commission to consider a number of options, including an employe stock ownership plan, private investment and a requirement that the states subsidize some of the system. The commission, to be headed by former Illinois governor Richard Ogilvie, was asked to report within eight months.

Response to yesterday's announcement was lukewarm. Sen. Frank R. Lautenberg (D-N.J.), who chairs the Senate Appropriations transportation subcommittee, said that he would prefer to see the commission study ways that Amtrak could be operated more efficiently.

"Any proposal to dismantle Amtrak will be soundly rejected by Congress," Lautenberg said.