MIAMI — Rick Scott, businessman turned politician, campaigned for governor in 2010 with promises to run Florida like a successful business — more efficiency, lower costs, less hand-wringing and measurable results.

He meant higher education, too, but until recently that meant mostly shrinking budgets.

Now, looking for more value on the remaining dollars, Governor Scott and Republican lawmakers are prodding Florida’s 12 state universities to find ways to steer students toward majors that are in demand in the job market.

The message from Tallahassee could not be blunter: Give us engineers, scientists, health care specialists and technology experts. Do not worry so much about historians, philosophers, anthropologists and English majors....