Question: Q. 1. (25 Pts) A Small Engineering Consulting Firm Is Establishing Its Plan For The Next Year. The Director And The Partners….

Transcribed image text: Q. 1. (25 pts) A small engineering consulting firm is establishing its plan for the next year. The director and the partners are to decide which projects to pursue. Preliminary research has been done on 8 projects and they have estimated the profit that project i will bring (p; dollars), work days required for project i (d:), and CPU time in hours) required for project i (t;), i = 1,…, 8. The company has 1000 CPU hours available for the next year. There are currently 10 engineers available to work on the projects and they work 240 days in a year. The firm has 3 partners and each project can be supervised by exactly one partner. A partner can be responsible for at most 2 projects. The firm want to maximize the next year’s profit and they need to decide which projects to undertake and by whom they are supervised. (a) [15 pts] Provide an integer programming model for this problem. Consider the following additional requirements independently. Define new decision variables when necessary. (6) [2.5 pts] The director has 4 favorite projects: 3, 4, 7 and 8. At least one of them should be selected (c) [2.5 pts] Either at least one of the projects 1,2 and 3 or at most one of the projects 5.6, 7 should be selected. (d) [2.5 pts] Partner I cannot supervise projects 3 and 6 together. (e) [2.5 pts] If Partner 2 supervises project 3 or 4 (or both) then Partner 3 should supervise project 5.