Quantitative Decision Models Exam

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TIME: 3 hours (180 minutes) PAGES: 20 (including this cover page)

INSTRUCTIONS: 1. Total Mark Value: 100 Number of questions: 7 2. 1 page (single-sided-letter-sized) notes are permitted. 3. Stand-alone-non-programmable calculators are permitted. 4. Budget your time carefully. 5. Answers are to be given in the space provided. However, should you require additional space for a complete answer, use the blank page attached for this purpose. 6. For all problems where calculation space is provided, show your reasoning and work. Unsubstantiated answers will usually receive no marks. 7. You are to stop writing immediately upon being told that the exam is over. The exam time includes the time to write your name. If you fail to stop immediately, a penalty will be applied. TOTAL MARKS Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 TOTAL 16 15 13 16 14 6 20 100 MARKS RECEIVED

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Question 1 Graphical solution (16 marks) For a linear programming model given below: Decision variables x1  Units of product 1 to produce. x2 – Units of product 2 to produce. Objective function Maximize 4.0x1 + 3.6x2 Constraints Constraint 1: 11x1 + 5x2 > 55 Constraint 2: 3x1 + 4x2 < 36 Constraint 3: 4x1 – 9x2 < 0 Nonnegativity: x1, x2 >= 0 Solve this linear programming model by using the graphical approach (Graph paper is provided on the next page). For your graphical solution,  Label the axes.  Draw and label each constraint. Show your procedure of drawing Constraint 3 only.  For each constraint line, determine and label which side is feasible. Briefly explain how to determine the feasible side for Constraint 3 only.  Shade and label the feasible region.  Identify all feasible corner points and determine the coordinates of each feasible corner point. Show only your calculations for the corner point determined by Constraints 1 and 2.  Determine the optimal solution and objective function value.  For all calculations in this question, please