Question: PLEASE DO D), E), F), G) 6. Consider the two-variable knapsack problem: max4x+3y subject to 5x+6ya7+a8+a9+6,x,y{0,1,2,3}. The values a7,a8 and a9 are the last 3

PLEASE DO D), E), F), G) 6. Consider the

PLEASE DO D), E), F), G)

6. Consider the two-variable knapsack problem: max4x+3y subject to 5x+6ya7+a8+a9+6,x,y{0,1,2,3}. The values a7,a8 and a9 are the last 3 digits of your student id. (a) Sketch this problem, showing the integer feasible set. (b) What is a suitable LP relaxation for the problem? Include the LP feasible region in your sketch. (c) Find the optimal solutions to the integer program and its LP relaxation. (d) Form the Lagrangian relaxation (IP(u)) for this problem by dualizing the knapsack constraint with parameter u. 408 and 708 Page 3 of 4 (e) Explain how to solve (IP(u)) without using the simplex method. Your algorithm should depend on the objective function, which you can take to be c1x1+c2x2. (f) What range of values of u should we consider? (g) What value of the parameter u gives the strongest Lagrangian relaxation

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