EPM945 OPTIMIZATION AND DECISION MAKING - COURSEWORK Assignment set on Friday, 3 December 2021. Completed assignment, to

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Epm945 Optimization And Decision Making Coursework Assignment Set On Friday 3 December 2021 Completed Assignment To 1 (52.67 KiB) Viewed 59 times

EPM945 OPTIMIZATION AND DECISION MAKING - COURSEWORK Assignment set on Friday, 3 December 2021. Completed assignment, to be handed in by Tuesday, 4 January 2021 on Moodle by 4.00 pm. Late submissions will be penalised. Answer all questions. Show all necessary working. Question 1 Consider the primal linear programming problem below. Maximise 81 + x2 + 5/4.23, subject to 8.01 +3.x2 + 6.13 < 12, 6.71 + 162, +12.73 < 20. 21,22,13 > 0 a) Construct the dual problem and solve it graphically. b) Determine a solution to the primal problem, stating clearly any results that you use. (12 marks) Question 2 Use the simplex method to solve the following simplex problems. a) Maximise 6x + 9x2 +6.0; subject to 311 + 2x2 + 13 < 6, 21 +22 +234, X +3.02 +3.03 <10 11,12,13 > 0 b) Maximise-5.6'1 - 2 - 3.73 subject to 21 + 7.62 <1, 2.01 +4.02 - 13 <0, -321 +39 - 2x3 < -2 21, 22, 23 > 0 c) Maximise 5.21 +29+ 4.63 +3.74 subject to 21 +222 +33 +34 < 6, -21 +229 + 4x4 = 1. 21 +3.ry = 6 23 unrestricted, 21, 22, 24 > 0. (15 marks) 1