The hint is at the end. Please give me the answer of a b and c in details. Also, b needs a network diagram.

In a Word document, state the algebraic formulation (identify the decision variables, the objective function and the constraints) for each problem and answer the questions in the problems. Attached the Excel spreadsheet model (with Answer Report and Sensitivity Report) for each problem to support your answers. Use formatting (labels, colors, borders) to enhance the readability of your models. 3.8 Cash Planning: A startup investment project needs money to cover its cash flow needs. The cash income and expenditures for the period January through April are as follows. Month January February March April Total Cash flow ($000) -150 -450 500 250 150 At the beginning of May, all excess cash will be paid out to investors. There are two ways to finance the project. One is the possibility of taking out a long-term loan at the beginning of January. The interest on this loan is 1% per month, payable on the first of the month for the next 3 months. This loan can be as large as $400,000; the principal is due April 1; and no prepayment is permitted. The alternative is a short-term loan that can be taken out at the beginning of each month. This loan must be paid back at the beginning of the following month with 1.2% interest. A maximum of $300,000 may be used for this short-term loan in any month. In addition, investments may be made in a money market fund at the start of each month. This fund will pay 0.7% interest at the beginning of the following month. Assume the following about the timing of cash flows. For months in which there is a net cash deficit, sufficient funds must be on hand at the start of the month to cover the net outflow. For months in which there is a net cash surplus, the net inflow cannot be used until the end of the month (i.e., the start of the next month). (a) What is the maximum amount that can be returned to investors? What is the optimal amount of money to borrow from each of the potential loan sources? (b) Show the network diagram corresponding to the solution in (a). That is, label each of the arcs in the solution and verify that the flows are consistent with the given information. (c) Explain the cost of funds for each month in the planning period. That is, if there were a $1000 change in the cash flows for any month, what would be the dollar change in the amount returned to investors? Hint for 3.8 Here is an Excel sheet with the information stated in the problem assuming that they borrow the maximum in the first month using the long-term loan, and then whatever it is necessary to cover any deficit in the following months with the short-term loan. The sheet shows a feasible solution. Your job is to find the optimal solution; that is, how much to borrow long-term and short-term to maximize the return to investors. Cash Planning Max Long-term Short-term Money Market Interest Available 400 1% January 300 1.20% Any month 0.70% Month Cash Flow Long Term $ (150.00) $ 400.00 $ (450.00) January February March April May Long Term Short Term Money Short Term Balance P&I P&I Market 300.00 $ 550.00 300.00 (4.00) $ (303.60) $ 553.85 $ 96.25 300.00 $ (4.00) $ (303.60) $ 96.92 $ 89.32 300.00 $ (404.00) $ (303.60) $ 89.95 $ 182.35 $ (303.60) $ 183.63 $ 130.03 A A A A $ 500.00 $ 250.00 In a Word document, state the algebraic formulation (identify the decision variables, the objective function and the constraints) for each problem and answer the questions in the problems. Attached the Excel spreadsheet model (with Answer Report and Sensitivity Report) for each problem to support your answers. Use formatting (labels, colors, borders) to enhance the readability of your models. 3.8 Cash Planning: A startup investment project needs money to cover its cash flow needs. The cash income and expenditures for the period January through April are as follows. Month January February March April Total Cash flow ($000) -150 -450 500 250 150 At the beginning of May, all excess cash will be paid out to investors. There are two ways to finance the project. One is the possibility of taking out a long-term loan at the beginning of January. The interest on this loan is 1% per month, payable on the first of the month for the next 3 months. This loan can be as large as $400,000; the principal is due April 1; and no prepayment is permitted. The alternative is a short-term loan that can be taken out at the beginning of each month. This loan must be paid back at the beginning of the following month with 1.2% interest. A maximum of $300,000 may be used for this short-term loan in any month. In addition, investments may be made in a money market fund at the start of each month. This fund will pay 0.7% interest at the beginning of the following month. Assume the following about the timing of cash flows. For months in which there is a net cash deficit, sufficient funds must be on hand at the start of the month to cover the net outflow. For months in which there is a net cash surplus, the net inflow cannot be used until the end of the month (i.e., the start of the next month). (a) What is the maximum amount that can be returned to investors? What is the optimal amount of money to borrow from each of the potential loan sources? (b) Show the network diagram corresponding to the solution in (a). That is, label each of the arcs in the solution and verify that the flows are consistent with the given information. (c) Explain the cost of funds for each month in the planning period. That is, if there were a $1000 change in the cash flows for any month, what would be the dollar change in the amount returned to investors? Hint for 3.8 Here is an Excel sheet with the information stated in the problem assuming that they borrow the maximum in the first month using the long-term loan, and then whatever it is necessary to cover any deficit in the following months with the short-term loan. The sheet shows a feasible solution. Your job is to find the optimal solution; that is, how much to borrow long-term and short-term to maximize the return to investors. Cash Planning Max Long-term Short-term Money Market Interest Available 400 1% January 300 1.20% Any month 0.70% Month Cash Flow Long Term $ (150.00) $ 400.00 $ (450.00) January February March April May Long Term Short Term Money Short Term Balance P&I P&I Market 300.00 $ 550.00 300.00 (4.00) $ (303.60) $ 553.85 $ 96.25 300.00 $ (4.00) $ (303.60) $ 96.92 $ 89.32 300.00 $ (404.00) $ (303.60) $ 89.95 $ 182.35 $ (303.60) $ 183.63 $ 130.03 A A A A $ 500.00 $ 250.00