Question

When the door of the Chapel of the Mausoleum in Hamilton, Scotland, is slammed shut, the last echo heard by someone standing just inside the door reportedly comes 23.0 s later, (a) If that echo were due to a single reflection off a wall opposite the door, how far from the door would that wall be? (b) If, instead, the wall is 25.9 m away, how many reflections (back and forth) correspond to the last echo? Assume the speed of sound is 345 m/s.

Answer 1

Given linear programming problem Maximize Z = - 5x_1 + 5x_2 + 13x_3 subject to - x_1 + x_2 + 3x_3 lessthanorequalto 20 12x_1 + 4x_2 + 10x_3 lessthanorequalto 90 x_1, x_2x_3 lessthanorequalto 0 change the inequalities into a standard form, by using slack variables x_4 and x_5 Maximize Z = - 5x_1 + 5x_2 + 13x_3 subject to - x_1 + x_2 + 3x_3 + x_4 + 0 . x_5 = 20 12x_1 + 4x_2 + 10x_3 + 0 + x_4 + x_5 = 90 x_1, x_2x_3 construct following simple table Min{20/-1 90/12} = - 20 So, the leaving variable is X_4 entering variable is x_1 and the pivot element is 12/- 1 = - 12 Now construct the second table as follows From the second table Z_j - C_j lessthanorequalto 0 hence the optimality is satisfied The maximum value is 100 and the non basic variables x_1 and x_2 have zero inZ_j - C_j in row So