Mathematical Models

Homework Assignment #6

Due Wednesday, April 16, 11:00 am

Homework should be turned in at the BEGINNING OF CLASS. Unless otherwise specified, all problem numbers refer to Giordano, Weir and Fox, the required text for the course. You should write up solutions neatly to all problems, making sure to SHOW ALL YOUR WORK. A nonempty subset will be graded. You are strongly encouraged to work on these problems with other classmates, although the solutions you turn in should be your own work. At the top of your homework, please list any students you work with or any other resources you found helpful (websites, books, faculty, etc.)

Section 7.1
Problems:   1, 4

Note: Once you have your model (with constraints and objective functions) state whether it is a linear program or not.

Section 7.2
Problems:   1, 2, 4a

Note: Solve these problems using the geometric techniques discussed in class.

Section 7.4
Problems:   1, 2

Note: Solve these problems (the same one's as in Section 7.2) using the Simplex method.

Section 7.5
Problems:   1

Note: Following the argument given in the text, vary c_2, the profit earned from each bookcase sold, and determine what effects this has on the total profit and on the optimal extreme point for the corresponding linear program. Summarize your results carefully, breaking your answer into different cases depending on the value of c_2.