Name(last, frist) ID: no aids allowed, time allowed 30 min. total mark: 24 (+2 bonus marks) apm236 Quiz 1. Consider the LPP: minimize z = 2x1 + x2 subject to the constraints x1 + x2 4 x1 2x2 1 x1 0, x2 unrestricted. a) (6 marks) Draw the feasible region presented above, determine the extreme points, and use the extreme point theorem to solve the LPP. b) (6 marks) Convert this problem to the Canonical form. 1 Name(last, frist) ID: apm236 Quiz 2. (6 marks) Prove that the feasible region of a LPP determined by Ax = b (in Canonical format,) is convex. 3. (8 marks) First give the denition of an extreme point, and then show that if a point x is not an extreme point of the feasible region, and if the optimal solution is unique then the point x cannot be the optimal solution. 2