HW1 solution

# HW1 solution - Solution of Homework 1 Problem(1 Solution We...

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Solution of Homework 1 Problem (1): Solution: We want to find the coefficients x 1 , x 2 , and x 3 such that b (0) = 1 , b (2) = 7 , and b (5) = 46 . These three equations can be written in a matrix form: 1 0 0 1 2 4 1 5 25 x 1 x 2 x 3 = 1 7 46 The solution is 1 1 2 s Problem (2): Solution: Let x 1 be the number of desks, x 2 the number of bookshelves, x 3 the number of cabinets with door, and x 4 the number of cabinets with drawers. Then the optimization can be formulated as Maximize 200 x 1 + 100 x 2 + 150 x 3 + 200 x 4 subject to 8 x 1 + 6 x 2 + 2 x 3 + 4 x 4 2000 12 x 1 + 10 x 2 + 25 x 3 + 20 x 4 6000 x 1 , x 2 , x 3 , x 4 0 s 1

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Problem (3) Solution: This is similar to problem (1). We want to find the coefficients x 1 and x 2 such that b (0) = 3 , b (1) = 3 , and b (1) = 6 . These can be written in a matrix form: Ax = b with A = 1 0 1 1 1 1 and b = 3 3 6 But there is no solution for this system of equations. In this case, we
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## This note was uploaded on 01/11/2011 for the course MATH Math 164 taught by Professor Brown during the Summer '10 term at UCLA.

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HW1 solution - Solution of Homework 1 Problem(1 Solution We...

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