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# Tutorial 8 - NATIONAL UNIVERSITY OF SINGAPORE Department of...

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NATIONAL UNIVERSITY OF SINGAPORE Department of Mathematics MA3252 Linear and Network Optimization Tutorial 8 1. Consider the following primal LP problem: min 2 x 1 + x 2 + x 3 s.t. 3 x 1 + x 2 1 x 1 + 2 x 2 + x 3 4 x 1 , x 2 , x 3 0 (a) Determine the dual problem and solve it graphically. (b) Use the Complementary Slackness Optimality Conditions to find the primal optimal solution. 2. Solve the following linear programming problem by the dual simplex method. min 2 x 1 + 3 x 2 + x 3 s.t. 2 x 1 + x 2 30 - x 1 + x 2 + 2 x 3 10 x 2 + x 3 = 6 x 1 , x 2 , x 3 0 3. Show that choosing the entering variable by the minimum ratio will maintain the optimality condition (¯ c 0 for minimization) in the dual simplex method. 4. Fatimah’s drink stall sells three types of drink daily. Each type of drink is made from milk and rose syrup. Sixty litres of milk and twenty five litres of rose syrup are available daily. The composition of each type of drink per litre and the profit earned from each litre of drink is shown below: Drink

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