503_HW8_S11 - Variables and their meanings and bounds :...

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UML CS Algorithms 91.503 (section 201) Spring, 2011 Page 1 of 2 Homework #8 Assigned: Tuesday, 4/19 Due: Tuesday, 4/26 at 5:30 p.m. This assignment covers textbook material in Chapter 29 (Linear Programming). 1. (100 points) Consider the following problem : A textbook publisher is planning to bind the latest version of our textbook in 3 different bindings: 1) paperback, 2) book club, and 3) library. Each book goes through a sewing and gluing process. The time required for each process is given in the accompanying table: Paperback Book Club Library Sewing (minutes) 2 2 3 Gluing (minutes) 4 6 10 Now, suppose that the sewing process is available 7 hours per day and the gluing process is available for 10 hours per day. Also, assume that the profits are $0.50 on a paperback edition, $0.80 on a book club edition, and $1.20 on a library edition. How many books will be manufactured in each binding when the profit is maximized? a) (30 points) Formulate this problem as a linear program by filling in the parts below:
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Unformatted text preview: Variables and their meanings and bounds : Objective : minimize maximize (circle one) Linear objective function : subject to: (list your constraints) UML CS Algorithms 91.503 (section 201) Spring, 2011 Page 2 of 2 Note : It is acceptable to produce a fractional amount of a book. b) (10 points) Put your formulation from (a) into standard form. c) (10 points) Convert your answer from (b) into slack form. d) (30 points) Using your answer to (c), solve the linear programming formulation of this problem using the SIMPLEX method. Show the optimal value of the objective function and the associated values of the variables. e) (10 points) Form the dual of your answer to (c). f) (10 points) Now, suppose that we fix the number of books in library binding to 5. Solve your linear programming model from (a) (with this additional constraint) using a method of your choice. In your solution, show the value of the objective function and the values of all of the variables....
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503_HW8_S11 - Variables and their meanings and bounds :...

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