(1) Government has $30 million available for the coming year to allocate to three governmental agencies. Because of some commitments, the government established a minimal level of funding for each agency. These funding levels are $3 million, $5 million, and $8 million, respectively. The second agency cannot utilize more than $17 million without major new capital expansion and the government is unwilling to undertake such an expansion at this time. Each agency has the opportunity to conduct various projects with the funds it receives. A rate of return, as a percent of the investment, has been established for each project and the government wants to have the most possible return from the projects. Additionally, certain projects permit only limited investment. The data for each project are given below: Agency Project 1 2 3 4 Rate of Return Upper limit of investment 7% $6 million 5% $5 million 8% $9 million 5% $7 million 7% $10 million 9% $4 million 10% $6 million 8% $3 million 2 5 6 7 8 3 Formulate this problem as a linear program. (2% of final grade) (a) Write the decision variables and give the meaning of each decision variable. (0.5%) (b) Write the objective function. (0.5%) (c) Write the constraints and state the meaning of each constraint. (0.5%) (d) Write the whole LP model. (0.5%)