You have n balloons, each with a certain capacity for holding air. For every i, i =1, . , n, there is exactly one balloon with capacity 1/i.

You have n balloons, each with a certain capacity for holding air. For every i, i =1, . . . , n, there is exactly one balloon with capacity 1/i. The balloons look identical,and you cannot tell the capacity of any of them just by looking at it. Your goal is to inflate the balloons to the maximum total value possible. At every step, you can pick a balloon and decide how much air to put in it. (This could be one that already contains some air.) If you do not exceed the capacity of the balloon, you get a reward equal to the amount of air you used. If you exceed the capacity, the balloon pops and you get nothing, but you do find out its capacity.a) Find a deterministic strategy that guarantees a reward of 1.b) Find a randomized strategy with an expected reward that is strictly greater than 1.