Does a Social Contract Obligate the State to Act in a Utilitarian Manner?

I will preface this with my background. Please remember that I'm a noob at this stuff. :)

I'm in medical school. Physicians, generally speaking, prefer consequentialist ethical outlooks (Veatch, The Basics of Bioethics, 2000). For whatever reason, that intuitively does not sit right with me, which led to argument with another student about a cognitively impaired patient we had.

In any case, that was when I began looking into philosophy and ethics. I had started reading about social contract theories, which led to this problem.

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Let's presume that people enter into a social contract with a state to preserve their natural rights.

Would this obligate the state to act in a manner to preserve the natural rights of as many contractees as possible?

For example: Would the state have to take wealth from people to fund antipollution or preventative health initiatives, which would secure the lives and natural rights of many more people than those whose rights it abrogates?

For another one: Let us presuppose that a false acquittal eventually leads more crimes, and thus worse consequences, than a false conviction. If it would secure more people's natural rights, would the state have to implement judicial policies to find more criminals guilty, even at the cost of punishing innocents?

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My initial answer was "no." That's why we have prohibitions on things like unreasonable search/seizure, no matter how good the consequences may be.

But I cannot figure out a way to tie this back into the social contract. It seems intuitive from that perspective that the state should act to maximize the rights of as many people that have trusted it.

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So my questions are:

Does a social contract obligate the state to act in a utilitarian manner?

If not, is there a conception of a social contract that would preserve people's rights against state abrogation, even if more people would lose such rights (from an other party abrogating them)?

If not, is there an alternate discourse that would allow it?

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Thanks in advance!