Need mathematical model representation in terms of objective function, variables and constraints

3. Consider the following scenario: You have one bipartite graph where the size of one partition is higher than the other partition. For each edge of this bipartite graph, there are two weights associated (there are no relationships between these two weights). We can call these two weights as Cij and Rij where (1,j) is an edge. It means that if i and j are matched at the end, we need to pay a cost Cij but we will get some reward as Rij. The goal is to match these vertices from two partitions in such a way so that we pay the minimum cost while the total sum of rewards that we will get from these matching is more than a threshold Z. Please note that, one node from one partition can be maximum matched with one node of another partition Now, first write down an ILP/LP formulation for the optimal solution for this problem. 3. Consider the following scenario: You have one bipartite graph where the size of one partition is higher than the other partition. For each edge of this bipartite graph, there are two weights associated (there are no relationships between these two weights). We can call these two weights as Cij and Rij where (1,j) is an edge. It means that if i and j are matched at the end, we need to pay a cost Cij but we will get some reward as Rij. The goal is to match these vertices from two partitions in such a way so that we pay the minimum cost while the total sum of rewards that we will get from these matching is more than a threshold Z. Please note that, one node from one partition can be maximum matched with one node of another partition Now, first write down an ILP/LP formulation for the optimal solution for this