BIT2406FinalExamStudyGuide - BIT 2406 Quantitative Methods...

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BIT 2406 Quantitative Methods II – Spring 2010 Final Exam Study Guide Exam Information Date/Time : 10 May 2010, Monday, 11:05 AM – 1:05 PM Place : Torgersen 2150 Exam Type : Comprehensive. Closed everything : only pencil, eraser and simple calculator are allowed. # of problems : 40 = 8 (from chps 2, 3, 5) + 12 (from chps 6, 7, 8) + 20 from (chps 9, 12, 15) Curve : If the average is less than 80, the grades will be curved to bring the average to 80. How to study for Chapters 2 and 3 1- Write down two to three constraints with two variables x 1 and x 2 in the form of a x 1 + b x 2 ≥ c or x 1 + b x 2 ≤ c, write an objective function in the form of Z = a x 1 + b x 2 and assign random numbers between 0 and 10 for a, b and c. 2- Plot the constraints from step 1 and determine the feasible region. Identify the extreme points of the feasible region. Note that you may end up having no feasible region. In this case change one or more of your constraints and try again. 3- Plot the objective line passing through one of the extreme points. First consider that it is a maximization problem and find out the improvement direction for the objective line. Slide the objective line in the improvement direction without changing its slope. Observe the last point of contact between the objective line and the feasible region, which is the optimal solution to the problem. Repeat step 3 so far considering that it is a minimization problem. Note that the last point of contact can be a line, in which case there are infinitely many alternative solutions, or there may not be a last point of contact if the problem is unbounded. If you observe an unbounded case, change the constraints such that you have a finite solution. 4- After you find the solution in step 3, consider sensitivity of the objective coefficients. First write down the slope for each constraint and the objective function. Then visually observe the upper and lower bounds as the objective rotates around the optimal solution when you increase/decrease the objective coefficients. Based on your observations, calculate the upper bound and lower bound for the sensitivity range for each objective coefficient using the slopes. 5- Consider the sensitivity range for the right-hand-side (RHS) for each constraint based on the solution mix (the non-zero and zero partition of decision variables + slack/surplus variables). Visually observe how the solution changes as you increase/decrease the RHS and find the points that define the upper and lower bounds. Plug in those points in the left- hand-side to find the corresponding upper and lower RHS bounds for each constraint. 6- Plug in the same points from step 5 in the objective to find the corresponding objective function values for each constraint. Divide the difference between the objective function values by the difference between the upper and lower bounds to find the shadow price for each constraint. How to study for Chapter 5
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BIT2406FinalExamStudyGuide - BIT 2406 Quantitative Methods...

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