q1_cee3804_2011_solution

# q1_cee3804_2011_solution - CEE 3804 Computer Applications...

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CEE 3804: Computer Applications in Civil Engineering Spring 2011 Quiz 1 Solution Key Instructor: Trani The information provided in this exam is my own work. I have not received information from another person while doing this exam. Write your solutions in a single MSWord file. Cut and Paste all your answers using screen captures. Show all your work. Print and bring a hard copy to the class. Problem 1 (50 Points) An engineer formulates a linear programming problem as follows: Maximize z = 200 x 1 + 300 x 2 Subject to: x 2 1 2 x 1 25 ………………………………… (1) x 2 40 ………………………………… (2) x 2 + 4 x 1 = 220 ………………………………… (3) x 1 0 and x 2 0 a) Obtain a graphical solution. Clearly indicate the corner points and the optimal solution to the problem. Plot the line of constant maximum value of Z. CEE 3804 Trani Page 1 of 9

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Figure 1. Graphical Solution to the Problem. The optimal solution is point (x1,x2) to be (45,40) with a value of the objective function Z is 11,000 units. b) Find the optimal solution using the Simplex method (table approach) Write the problem in canonical form by adding slack and artificial variables as needed. See Course notes starting on page 21. Take one constraint equation at a time. First constrain equation. x 2 1 2 x 1 25 Revise to: x 2 1 2 x 1 + x 3 = 25 by adding a slack variable Second constraint equation. x 2 40 Revise to: x 2 + x 4 = 40 by adding a slack variable Third constrain equation. x 2 + 4 x 1 = 220 Revise to: CEE 3804 Trani Page 2 of 9
x 2 + 4 x 1 + x 5 = 220 by adding an artificial variable Revise the objective function.

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q1_cee3804_2011_solution - CEE 3804 Computer Applications...

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