# HW2 - substances: A B C D cost/kg in \$ Component 1 (gr/kg)...

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2. Homework for IEOR162 Linear Programming Semester: Fall 2010 Instructor: Dr. Sarah Drewes Due to: Tue, September 28, 2010 (at the beginning of class) P1 The management of a hospital requires the following number of nurses each day: time nurses required 0.00 a.m. to 4.00 a.m. 50 4.00 a.m. to 8.00 a.m. 60 8.00 a.m. to noon 40 noon to 4 p.m. 50 4 p.m. to 8 p.m. 30 8 p.m. to midnight 25 The nursing sta± is working in 8-hour-shifts, where each shift starts at 0 a.m., 4 a.m., 8 a.m., noon, 4 p.m. or 8 p.m. . The goal is to generate a work schedule that minimizes the number of nurses. Model this problem as an LP. Is the feasible region convex? P2 A company produces animal food that is a mixture of three di±erent ingredients: two nutrient-rich components and a ²lling component, that contains no nutritive substances. Each kilogram (1 kg = 1000 gr) of food must contain the following minimal amount of nutritive substances: 1

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nutritive substance A B C D gr 90 50 20 2 The nutritive components contain the following amounts of nutritive
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Unformatted text preview: substances: A B C D cost/kg in \$ Component 1 (gr/kg) 100 80 40 10 40 Component 2 (gr/kg) 200 150 20 – 60 We assume that the cost of the Flling component is negligible. The food mixture shall be produced with minimal costs. ±ormulate the problem as an LP. Graph the feasible region. Is the feasible region convex? P3 A company has two investments with varying cash²ows available. The cash²ows (in thousands of dollars) are given in the following table: Time 1 2 3 Inv. 1-6-5 7 9 Inv. 2-8-3 9 7 At time 0, there are \$ 10000 available for investment and at time 1 there are \$ 7000 available for investment. Assume that the interest rate is r = 0 . 1. Set up an LP whose solution maximizes the NPV obtained from these investments. Graphically Fnd the optimal solution to the LP. Assume that any fraction (less or equal to 100 %) of investment may be purchased. 2...
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## This note was uploaded on 01/21/2011 for the course IEOR 162 taught by Professor Zhang during the Fall '07 term at Berkeley.

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HW2 - substances: A B C D cost/kg in \$ Component 1 (gr/kg)...

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