# cee191-fa03-final-Madanat-exam - CE 152: CEE Systems...

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CE 152: CEE Systems Analysis Fall 2003 Final Exam (30 points) Professor Samer Madanat Problem 1 (6 points) Assume that the number of highway miles that can be resurfaced, H, is a function of both the hours of labor, L, and of machines, M: H = 0.5 L 0.2 M 0.8 (a) Minimize the cost of resurfacing 20 miles, given that the hourly rates for labor and machines are: C L = \$20; C M = \$160. (b) Interpret the meaning of the Lagrange multiplier in this problem.

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Problem 2 (9 points) City planners must decide the optimal allocation of fire stations to three districts. Zero to three stations may be located in a district. The table below shows the relationship between the number of stations and the annual expected property damage due to fires, based on statistical data. Differences among districts are due to population, construction materials, and so on. A budget constraint restricts the total number of stations to five. Number of stations per district

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## This note was uploaded on 12/01/2011 for the course CE 13972 taught by Professor Chow during the Spring '09 term at University of California, Berkeley.

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cee191-fa03-final-Madanat-exam - CE 152: CEE Systems...

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