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Briefly explain Mills greatest happiness principle and suggest what Mill would think we should do here.

A pandemic currently rages through the world. Not only are hundreds of thousands if not millions expected to die, but national economies have foundered badly. Nations are divided over which strategy to take: on the one hand, 1) they could continue to order their citizens to shelter in place. This means that businesses will remain shuttered and markets will continue to fare poorly, with rising unemployment and impending shortages in many walks of life, yet we can expect the death-rate from the virus to plummet. On the other hand, 2) they could remove the shelter-in-place orders and allow businesses to open. This means we would see markets rally and employment rise, though the expectation is that the overall death-rate would shoot up.
Briefly explain Mills greatest happiness principle and suggest what Mill would think we should do here. Be sure to cite instances of both positive and negative utility in formulating your answer.
Next, explain Kants categorical imperative and talk about how Kant would respond.
Who makes the best case? Why? Defend your reply at length.