Please plot the above in MATLAB and also provide the detail codes and explanation.
Given an integer programming problem, we begin by solving the corresponding continuous problem by the simplex method. If we obtain an all-integer solution, then we have solved the problem. If, however, one or more of the variables of the optimal solution does not have an integer value, then we choose one such variable on which to branch. That is, we form two further problems with a view to splitting the feasible region into two sub-regions. For example, in the integer garment problem, having solved the initial continuous problem and found that X1 is not integer at the solution, we could decide to branch on X1. In this case, we have a solution X1 = 33, so to progress towards an all-integer solution, we seek to reduce the feasible region by solving two further continuous problems: the original continuous problem with the added constraint X1 < 3 and the original continuous problem with the added constraint X2 < 4. Hence the name branch and bound. The process continues until no further progress can be made along a particular branch or because it becomes apparent that further progress would not offer any improvement on existing solutions. The following example illustrates the method.
Solve the reduced integer garment problem by the branch and bound method, that is, maximize Z = 500X1 - 400X2 subject to 8X1 + 5X2 < 42, 3X1 + 16X2 < 60, X1 > 0, X2 > 0, X1 is an integer, and X2 is an integer.