#  Problem 3 6 points consider the following all-integer...

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Problem 1 (4 points) Indicate which of the following is an all-integer linear program and which is a mixed- integer linear program. Write the LP Relaxation for the problem but do not attempt to Solve A) Since a mixed integer linear program is only when some of the variable are integers. This would be a mixed integer linear programming, x2 is an integer in the IP while x1 is not. B) Pure integer linear programming is when all the variables are integers and in this case all the variables are consider to be integers. Therefore, the linear programing model LP relaxation (IP) is obtained by dropping off all the integers of only having constraints 0-1
Problem 3 (6 points) consider the following all-integer linear program: a. Graph the constraints for this problem. Use dots to indicate all feasible integer solutions. b. Solve the LP Relaxation of this problem.
c. Find the optimal integer solution. Problem 4 (8 points) Consider the following all-integer linear program: 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). Problem 7 (10 points) The following questions refer to a capital budgeting problem with six projects represented by 0-1 variables x1, x2, x3, x4, x5, and x6: a.
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