Assume that n projects need to be executed, and this can be done at m different locations. The cost of executing project j, 1 jn, at location i, 1 jm is given by wij and the corresponding profit by pij. Moreover, each location i has a budget b; from which the projects to be executed at this location can be paid. a. Clearly, the management of the plant likes to execute each project and wants to maximize profit. Introduce the decision variables and formulate the associated integer linear programming problem. b. Suppose it is not clear whether all projects can be executed due to budget restrictions. As in part (a), the management likes to maximize profit. Formulate now the associated integer programming problem.