Indexes can improve search times. However, there is some overhead when inserting or deleting a record to maintain the index correctly. Having too many indices can magnify the time impact. Suppose as an oversimplified example that if we have S indices, the expected time to find a record is 3-S seconds while the insertion/deletion time is 0.1*(S + 1) seconds. If on average, there are 100 lookups for every insertion/deletion, what value of S gives the minimum expected time per operation? Show your work.