What's the evolution of the phrase "milk it for all its worth"?

The phrase "milking it" seems to have originated in the context of finance. According to the OED, "milking" can refer to

The manipulation of funds for (esp. unscrupulous or illicit) financial gain; (more generally) exploitation of resources.

Similarly, given what the physical act of milking some animal is like, it makes sense to think about "milking it" as "getting as much as possible out of a resource."

All of this makes sense. I'm wondering, however, when this idiom started to be used in different contexts. When did it become common to hear "You're really milking that for all its worth" in reference to an injury, for example, or for an emotional slight?

Similarly, which is preferable: "milking it for all its worth" or "milking it for all it's worth"? Should there be a standard, or does it depend on the meaning one wants to convey? I'm inclined to prefer its, as a thing does possess a finite worth (theoretically).

The OED has its two relevant citations under this definition (10) of the verb 'milk':

Originally in the performing arts: to exploit (a scene, situation, line, etc.) for fullest effect; to elicit a favourable or appreciative reaction from (an audience) and contrive to prolong it as long as possible. Also in extended use.

The two citations are from 1950:

My feeling about the story is that you have got hold of something big, but have not yet milked it for all it is worth.

and 1971:

They milked the applause for all it was worth, then Bart held up his hand again.

As for ‘its’ v. ‘it’s’, it has never occurred to me that it might be anything other than the second, and the two citations support that view.

(Which edition of the OED are you using, ect? I can't find the definition you quote in the online edition which I use at http://www.oed.com/.)

I suspect this slang orginated in argicultural practices, where milking of cows, usually done twice daily, can provide slightly greater yields when performed 3 times daily. You get a bit more milk for a lot more work, so if you're really "milking" that cow, you're doing it to excess, with marginal benefit.