Need help with the question from (a) to (e).

1.4 Consider the integer linear program maximize x + 2y subject to 3x + 4y 0, y> 0 with x, y integers. (a) The optimal solution to the linear program (without the integer re- strictions) is r = 1.6, y = 1.8. Show that rounding this solution leads to an infeasible solution. (b) Starting from x = 0, y = 0, systematically enumerate all possible integer solutions and pick an optimal solution. Is it unique? (c) Replace the first inequality by 3x + 4y 0, y> 0 with x, y integers the optimal solution is r = 0, y 4/3. Rounding this results in the feasible solution x = 0, y = 1. Show that this is not optimal by finding the optimal feasible integer solution. 1.4 Consider the integer linear program maximize x + 2y subject to 3x + 4y 0, y> 0 with x, y integers. (a) The optimal solution to the linear program (without the integer re- strictions) is r = 1.6, y = 1.8. Show that rounding this solution leads to an infeasible solution. (b) Starting from x = 0, y = 0, systematically enumerate all possible integer solutions and pick an optimal solution. Is it unique? (c) Replace the first inequality by 3x + 4y 0, y> 0 with x, y integers the optimal solution is r = 0, y 4/3. Rounding this results in the feasible solution x = 0, y = 1. Show that this is not optimal by finding the optimal feasible integer solution