4. Assume that n projects need to be executed, and this can be done at 77 different locations. The cost of executing project j, 1 jn, at location 1, 1 7 m is given by way and the corresponding profit by pj. 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 likess 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.

1. Axsume that, n projoxts nesd to be cxcouted, and this can be done at m different. loentions. The cost. of excxating project 1,1yn, at location i, 1tm is given by as and the corrosirondirig protit by py. Moremer, cach locatican 2 has a ladget b from which the projcets to be coceuted ut this location ean be pali. a. Clearly, the manmgement of the plant likss to coxceute emel project and wants tor masimaze profit. Introduee the decision variablos ind formulate the thsociated integer lincar progmatmming prohlerr