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Suppose that you can rent time on a supercomputer that does 1 operations per second, and that the rental is $3000/hr. your company is willing to spend $17000 to solve the largest version of a certain problem it can.

a) if the best algorithm you know for solving this problem takes 5^n operations, where n is the size of the problem, what is the largest size you can solve?

b) suppose that someone discovers an algorithm for the same problem that takes n^{5} operations. what size problem can you solve now?

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