The board of directors of the Massachusetts Department of Transportation voted last week to award a $45 million contract for design and project management for early construction on the Green Line Extension. The contract was awarded to a joint venture between AECOM Technical Services Inc. of Los Angeles and HNTB, an infrastructure design company with a Boston office. In addition to overseeing the initial design for the railways, retaining walls, landscaping, and the network of electronic track switches and train controls, the companies will provide supporting documents required for the project to obtain federal New Starts funding. If the federal grant application is successful, the Federal Transit Administration could provide $400 million to $500 million, nearly half the project’s cost.