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IEOR 160-practice final Solution-1

IEOR 160-practice final Solution-1 - IEOR 160 Final...

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IEOR 160 – Final Practice Questions Solution Spring 2009 Problem 1 Three cities are located at the vertices of an equilateral triangle. (That is, the distance between any two cities is the same as the distance between any two other cities.) An airport is to be built at a location that minimizes the total (straight-line) distance from the airport to the three cities. Clearly define the variables needed for this problem and formulate the objective function. You need not solve the problem. Solution Assume on the axes of coordinate, the three cities lie in (0, 0), (0, a), (a/2, 3 1/2 a/2). Suppose we build the airport at (x, y). Then we can formulate the problem into Min (x 2 +y 2 )+(x 2 +(y-a) 2 )+((x-a/2) 2 +(y-3 1/2 a/2) 2 ) Problem 2 Consider the following project data: Activity Predecesso rs Duration (days) A - - 4 B - - 5 C A 16 D B 11 E A, B 17 F D, E 7 a. In the space below, draw the project network with activities on nodes .

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b. Compute each activity's EST (earliest starting time), LST (latest starting time) and slack.
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