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# hw3 - been hired Employees will be hired and then ﬁred at...

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EECS 250 – Digital Signal Processing I Fall 2009 Homework 3 Due: Thurs. October 29 1. 3.14-27 2. 3.14-28 3. 3.14-29 4. 3.15-30 5. 4.5-29 6. For the following matrix, A = 1 1 1 2 1 1 4 1 1 , answer the following questions: (a) Does the equation Ax = y have a solution for y = [2 3 5] T ? (b) If there is more than one solution, give a simple way of describing the family of all solutions. (c) Repeat (a) and (b) for y = [2 3 6] T . (d) How many linearly independent columns does A have? How many linearly independent rows? (e) Repeat (a)-(d) for the matrix obtained by changing the (2,2) entry in A from 1 to 2. 7. Suppose we are to set up a special manufacturing company which will operate for only 10 months. During the ten months, the company is to produce 1,000,000 copies of a single product. We assume that the manufacturing facilities have been leased for the 10-month period, but that labor has not yet
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Unformatted text preview: been hired. Employees will be hired and then ﬁred at some time during the 10-month period. The problem is to determine how many employees should be hired and ﬁred in each of the 10 months. Assume that each employee produces 100 items per month. The cost of labor is proportional to the number of available workers, but there is an additional cost due to hiring and ﬁring. If u ( k ) workers are hired in the k th month (negative u ( k ) corresponds to ﬁrings), the processing cost can be argued to be u 2 ( k ). At the end of the 10-month period, all workers must be ﬁred . Set up this problem as a min-norm problem that can be solved using the dual approximation theorem of Chapter 3. Then ﬁnd the solution u ( k ) for k = 1 , ··· , 10....
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