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Question - the book is named a ( Introduction to operations research) Document Preview: AMTH501 Assignment 1 Due: 24th of November, 2013 Question 1 For each of the following constraints, draw a separate graph to show the non-negative solutions that satisfy this constraint. 1. x1 + 3x2 6 2. 4x1 + 3x2 12 3. 4x1 + x2 8 4. Combine these constraints into a single graph to show the feasible region for the entire set of functional constraints plus non-negativity constraints. Question 2 Given the following objective function for a linear programming model maxZ = 2x1 + 3x2 1. Draw a graph that shows the corresponding objective function lines for Z = 6, Z = 12, and Z = 18. 2. Find the slope-intercept form of the equation for each of these three object ...Read More ive functions lines. Use a table to compare the slopes and the intercepts for these three lines e.g., Slope-intercept form Slope Intercept Z = 6 Z = 12 Z = 18 1 Question 3 Use the graphical method to solve the problem: max Z = 10x1 + 20x2 s.t. - x1 + 2x2 15 x1 + x2 12 5x1 + 3x2 45 and x1 0 x2 0 Question 4 The shaded area in the following graph represents the feasible region of a linear programming problem whose objective function is to be maximised. x1 x2 b b b b b b b b b b bbbbb bb b b (6, 0) (3, 3) (6, 3) (0, 2) (0, 0) Label each of the following statements as True or False, and then justify your answer based on the graphical method. In each case, give an example of an objective function that illustrates your answer. 1. If (3, 3) produces a larger value of the objective function than (0, 2) and (6, 3), then (3, 3) must be an optimal solution. 2. If (3, 3) is an optimal solution and multiple optimal solutions exist, then either (0, 2) or (6, 3) must also be an optimal solution. 3. The point (0, 0) cannot be an optimal solution. 2 Question 5 The following table summarises the key facts about two products, A and B, and three resources Q, R, and S, required to produce them. Resource Usage Resource per Unit Produced Amount of Resource Product A Product B Available Q 2 1 2 R 1 2 2 S 3 3 4 Profit per unit 3 2 All the... ...Read Less




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