The trustees of the University of Massachusetts authorized UMass president Robert L. Caret Wednesday to raise tuition and fees up to 4.9 percent next year if the Legislature fails to approve a proposed $39 million funding increase. The House has approved Governor Deval Patrick’s plan for $479 million in funding for the five-campus system. The Senate is proposing a budget of $455 million. Chairman Henry M. Thomas III said trustees felt that the vote was necessary. “Because the state budget has not been finalized, we find ourselves with the need to give President Caret the authority to raise tuition and fees if, and only if, state funding comes in at a figure lower than the $479 million proposed by the governor and already approved by the House,” Thomas said.