2) INTEGER PROGRAMMING (PROJECT SELECTION) (30 points) A company manager should choose from among 10 different existing projects to protect the future of the company from unexpected damages. Each project has a profit value and each project has a cost value. The parameters, the decision variables, the objective function, and the total budget constraint are given as follows: Pj = Profit that the company will obtain if they invest in project j. j = {1,...,10} C; = Invetment cost of the project j. j = {1,...,10} Q = Total available bugdet X; = {1, if the project i is selected by the manager, 0 otherwise.j = {1, ... ,10} Maximize Z = 2j-1P; * X; Total bugdet constraint -19; * X;