In which 1976 case did the supreme court determine that prison officials have a duty to provide medical treatment to inmates since inmates are dependent on them to provide for their medical needs?

The answer is: Estelle V. Gamble

Before the case, prison inmates were treated inhumanely. They often given rotten foods for their meals which cause physical harm to many of them and the government had no responsibility to took care of them when they're sick because they believed it was a 'waste of resource'