2. Assignment problem (i) 'CREATE', a design firm, has five teams, T1, T2... T5, that it wishes to assign to five new projects P1, P2...P5. The costs associated with assigning each team to each project are given in the table below. (a) Define your decision variables and write the problem as a linear program. (b) Using excel, solve for the minimum cost assignment of teams to projects. What is the total cost of assignment? T1 T2 T3 T4 T5 P1 10,500 12,500 10,000 11,000 P2 11,000 12,000 9,000 11,500 10,000 P3 9,500 12,000 9,000 14,000 10,500 P4 12,000 10,500 9,500 13,500 11,259 P5 10,000 13,000 11,000 12,000 11,500 (ii) At short notice, Project 3 is cancelled by the client. In order to retain its staff, CREATE must pay a retainer fee of 5000 to any team not fully employed. Under these circumstances how would the company change its plans? Which team is kept on retainer? If the firm could afford to let staff go, without paying a retainer, what would be the solution? (In each case explain how you set up the problem and use Excel to solve, including relevant screenshots.)