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UNIVERSITY OF HONG KONGDEPARTMENT OF MATHEMATICSMATH2901 Operations Research IQuiz / Class Test 1October 03, 2013 (Thursday)1. (10%)Let (P) denote a linear (min) program in standard form withmconstraints,n(> m) variables and full row rank. Assume also that (P) has a non-empty boundedfeasible region.(a) Give a precisemathematicaldefinition of a basic feasible solution of (P).(b) Give a precisemathematicaldefinition of an extreme point of the convex polyhedronof (P).(c) Give a significant relationship between part (a) and part (b) above.2. (20%)Recall our Oil Blending Example in lecture. Its LP formulation is given byMaxP= 2H+ 1.5L-C-10Subject toH+L+C≤802H+L-2C≤402H-L-2C≤20H, L, C≥0.Suppose now you are specifically informed of a restriction that NO amount of H oil needsto be considered (in trying to find the least-cost blending).(a) Show how this restriction simplifies its LP formulation. Construct the LP convexpolyhedron for this (restricted) LP formulation and determine all the potential least-cost blending solutions. Give also these solutions’ binding hyperplanes.