Invest A company is planning to invest in three available projects. Investing in each project has the realized cash flows (in millions of dollars) as listed in the table below

Terms(6 months)	Cash Flow Project 1	Cash Flow Project 2	Cash Flow Project 3
Initial (Term 0)	-3	-2	-2.0
1	-1	-0.5	-2.0
2	-1.8	1.5	-1.8
3	0.4	1.5	1
4	1.8	1.5	1
5	1.8	0.2	1
6	5.5	-1	6

For example, Project 1 requires an initial cash outflow of $3 million, relatively smaller outflows continue in the first and the second terms, it begins paying a small return in the third term, and a final payback of $5.5 million in the sixth term. Today Invest A has $2 million in cash. At the beginning of each term (0,1,2,3,4,5,6) the company can, if desired, borrow up to $2 million at 3.5% (per term) interest rate providing that it will be paid back next term. Leftover cash earns 3% (per term) interest. For example, if after borrowing and investing at time 0, Invest A has $1 million, it would receive $30,000 in the first term as interest. The company’s goal is to maximize cash on hand after cash flows 3 years from now are accounted for. What investment and borrowing strategy should it use? Assume that the company can invest in a fraction of a project. For example, if it invests in 0.5 of Project 3, it has, for example, cash outflows of -$1 million at the time 0 and at the first term. However it is not possible to invest in a project more than 100%. Hint: Cash flow should be balanced for every term (i.e flow in = flow out).

a) (20 Pts.) Formulate a linear programming model to optimize the investment plan.

b) (20 Pts.) Solve the model using GAMS.

c) (10 Pts.) Submit an executive summary report