# hw04-nlp - Homework 4 NLP 1(from Winston pg 628 The energy...

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Homework 4 NLP ---------------------------------------------------------------- 1. (from Winston, pg 628) The energy used in compressing a gas in 3 stages from an initial pressure "I" to a final pressure "F" is given by the formula K*(sqrt(p1/I) + sqrt(p2/p1) + sqrt(F/p2) - 3) where K is some arbitrary positive constant. Formulate an NLP whose solution describes how to minimze the energy used in compressing the gas. a) Using the values I=1 (atmosphere) and F=10, solve the NLP numerically. b) Based on the optimal p1 and p2 values you got, write down a formula for the optimal p1 and p2 as a function of I and F. c) Prove that your conjecture is indeed optimal (take the gradient, etc.) ---------------------------------------------------------------- 2. The Shotspotter problem: Shotspotter has set up open-air microphones around a city like Oakland, CA. Each microphone records the time that a gunshot sound arrived at the microphone and reports it to a central computer, which then figures out where the gunshot must have been. Suppose you get data from sensors as follows: the (x,y) for each sensor

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hw04-nlp - Homework 4 NLP 1(from Winston pg 628 The energy...

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