Problem 4 (15 points) Tower Engineering Corporation is considering undertaking several proposed projects for the next fiscal year. The projects, the number of engineers and the number of support personnel required for each project, and the expected profits for each project are summarized in the following table: 1 2 Projects 3 4 5 6 Engineers Required 20 55 47 38 90 63 Support Personnel Required 15 45 50 40 70 70 1.0 1.8 2.0 1.5 3.6 2.2 Profit ($1,000,000s) Formulate an integer program that maximizes Tower's profit subject to the management constraints, which are listed below. (2 points) Define the decision variables: (1 point) Write the objective function: Max P1 + 1.8P2 + 2P3 + 1.5P4 +3.6P5 +2.2P6 (7 points; one point each) Write constraints for the following requirements: Statement of the Constraint A Use no more than 175 engineers Mathematical form of the constraint 20P1+55P2 + 47P 3 + 38P4 + 90P5 + 63P6 175 B Use no more than 150 support personnel 15P1 +45P2 +50P3 + 40P4 + 70P5+ 70P6150 C If either project 6 or project 4 is done, both must be done D Project 2 can be done only if project 1 is done P4-P6-0 P1-P20 E Project 2 must be done if project 3 is done F If project 5 is done, project 3 must not be done and vice versa G|No more than three projects are to be done. (2 points) Optimal Z= P3+P51 P1+P2+P3+P4 + P5 + P6 3 Pi=0 or 1 (3 points) Populate table with optimal values for DVs. Use a cell for each DV in this fashion: DV name = value