Question 4 In a concert hall, the ceiling can be described by the plane x + y + z = 30. An audio engineer is trying to fix a speaker on the ceiling. Assuming that the audience will be seated at the...

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Extracted text: Question 4 In a concert hall, the ceiling can be described by the plane x + y + z = 30. An audio engineer is trying to fix a speaker on the ceiling. Assuming that the audience will be seated at the origin (0,0,0), he wants to find the position on the ceiling such that the intensity the of the sound is strongest at position of the audience. Given that the intensity of sound is inversely proportional to the squared of the distance away from the sound source, by finding the formula of the sound intensity the audience at (0, 0, 0) will experience given that the speaker must be fixed on the ceiling x + y + z = 30, find the optimum position to fix the speaker so that the audience will experience maximum sound intensity. (a) (b) Apply Lagrange Multipliers now to solve this problem.