4 Marks 28 Question 7(a): LPP - Interpretation The following is the data for a Minimization Problem of a Linear Program in the Simplex Method. Minimize Z = 3x1 + 4x2, subject to 2x1 + 3x2 2 150 4x1 + 3x2 2 120 X: + X220 Assume usual notations for additional variables St, sa for conversion to Equality. 1. What would be the Co-efficient of the Artificial Variables in the Objective Function? Why? 2. Wills and sz be part of the Initial Solution? Why? See Page 18.4, Q.No.10 1. For a Minimization Problem, Artificial Variables will have +M' Co-Efficient, where M - Infinity Cost, le. Cost to be avoided in order to have a Feasible Solution 2. 5. & 5 being Surplus Variables of a 2 Inequality, will not form a Unit Matrix, and hence, will not be part of the Initial Program/ Solution 1 2 3 10 60 20 Question 7(b): Pareto Analysis 4 Marks The following information is given about the type of defects during a production period and the frequencies of their occurrence in a Spectacle Manufacturing Company: Defect No. of Items End Frame not equidistant from the centre Non-Uniform grinding of Lenses Power Mismatches 4 Scratches on the surface 110 5 Sports / Stains on Lenses 5 6 Rough Edges of Lenses 70 Frame Colours - shade differences 25 Construct a Frequency Table so that a Pareto Chart can be constructed for the defect type. Which areas should the Company focus on? 7