Consider the following all-integer linear program: Max 10x1 + 3x2 s.t. 6x1 + 3x2 < 40 3x1 + 1x2 < 11 x1, x2 > and integer a) Formulate and solve the LP Relaxation of the problem. Solve it graphically, and round down to find a feasible solution. Specify an upper bound on the value of the optimal solution. b) Solve the integer linear program graphically. Compare the value of this solution with the solution obtained in part (a). c) Suppose the objective function changes to Max 3x1 1 6x2. Repeat parts (a) and (b) consider the following all integer linear program: Max 10x1+3x2 6x1 +7x2< 40 3x1 + 1x2<11 x1,x2> 0 and integer a. Formulate and solve the LP Relaxation of the problem.Solve it graphically, and round down to find a feasible s b. Solve the integer linear program graphically. Compare the value of this solution with the solution obtained in c. Suppose the objective function changes to Max 3x1+6x2. Repeat parts (a) and (b). 6x1+7x2 =40 3x1+x2 =11 x1 x2 x1 x2 0 6.666667 5.714286 0 x1 x2 2.142857 5.285714 2.466667 3.6 0 3.666667 11 0 nd round down to find a feasible solution. Specify an upper bound on the value of the optimal solution. tion with the solution obtained in part (a) 12 10 8 6x1+7x2 =40 3x1+x2 =11 6 (2.46,3.6) 4 2 0 points x1 0 2.46 3.6 0 1 x2 5.7 3.6 0 2 3 4 5 6 value of objective function 10x1+3x2 17.1 35.4 36 7 8 The objective function is maximum at (2.46 , 3.6 ) So the optimal solution is at (2.46 , 3.6 ) 6x1+7x2 =40 3x1+x2 =11 8