DO NOT DO THE FIRST PART OF THE PROJECT. The answer is already given for it. Please do the part that is in the Section; Solve and Analyze the Problem Due Dec. 8th

(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 Rate of Return Upper limit of investment 1 7% $6 million 1 2 5% $5 million 3 8% $9 million 4 5% $7 million 2 5 7% $10 million 6 9% $4 million 7 10% $6 million 3 8 8% $3 million 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%) Solve and analyze the problem 12%: Due is on Wednesday, Dec 8, at 2pm. 1. Solve the LP using Excel, or some other software. (1%) 2. Result analysis; Explain the meaning of the solution. (2%) 3. Change at least two coefficients in your objective function, and carefully explain their corresponding economic interpretations. (2%) 4. Change at least two RHS parameters, and do sensitivity analysis to check their changing interval, in which current basis remains optimal.(2%) 5. Explain the shadow price and their economic interpretation. (2%) 6. Please add your code in the final project (Excel: copy your input and results screen) (2%) 7. Use the template in D2L for the final report. (1%) Linear programming model: Biji amount of money the goverment allocates to agency i for project j. max z = 0.07.211 +0.05.212 + 0.08.213 +0.05.224 +0.07.C25 + 0.09.226 +0.1.237 +0.08.238 s.t. 211 +212 +213 +224 +225 +226 +237 +238 = 30 (total amount of available funding) X 11 + X 12 + 213 > 3 (minimum level of funding for agency 1); 224 +225 +226 > 5 (minimum level of funding for agency 2); 237 +238 > 8 (minimum level of funding for agency 3); X 24 +225 +226