3. own a property development firm. You consider investing in three development projects, each of which...

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3. own a property development firm. You consider investing in three development projects, each of which will take 1.5 years, or six quarters, to complete. For each project, each quarter marks a completion milestone, which may incur costs (e.g., from buying building materials and paying wages) or generate income (e.g., if completed parts of the project are sold to buyers). The table below shows the projected cash flow stream for each project across the six Semester 1 S682 Fa2406 47 You Q4 Q5 820 -1.8 0.4 1.8 1.8 Q6 1.5 1.5 1.5 -1.8 column shows the amount that must be paid (negative numb 92406 1 2023 Leto2 s numbers) for each project at the start of the corresponding quarter, in units of millions of dollars. The last column shows the estimated value of the projects at the end of quarter 6. (Note: project B has negative value at the end since it is a condition to demolish the development at the end of the 1.5 years. Therefore for an initial investment of $2.5 million over two quarters, the project will earn $4.7 million over four cost $1 million to demolish at the end.) S6 but arters, S680 QBarters. A S6820, (b) 139 B th023 m (6 Q2 Q3 -1 -0.5 -2 This means that cash flows are reduced proportionally. For example, if you were to invest 40% into project A, the cash flow would be -1.2, -0.4, It is possible to invest a fractional amount into each project 6820 Se-0.72, 0.16, 0.72, 0.72, 2.2. However, once y the end of the projects. firm has certain amounts to invest at the start of each quarter, gir 2 action, it stays the same until 479240ou decide on your investment 0230 023 in the following table (in millions). Se which increase in value by 3% per quarter; also paid each quarter. me Make s end 5.5 -1 Q1 Q2 Q3 Q4 Q5 Q6 end 0.5 0.4 0.38 0.36 0.34 0.3 2 can supplement these amounts by borrowing money each quarter at an interest rate of 3.5% per quarter. You have borrowing capacity of $2 million each quarter. Any loan taken out at the start of a quarter must be paid back (including interest) at the end of the quarter. You can also choose to invest money in bonds, onds. Bond investments are 23 Sper in 2406ere is no limit for i ho23 Sesting i 470 our goal is to choose how much to invest in the projects, how much to borrow each quarter, and how much to invest in bonds each quarter in order maximize the net worth of your portfolio at the end of Q6. (a) (14 points) Formulate a linear program to find the optimal investment plan. Solve your linear program (using code from part (b)) and interpret the solution. 6. let Cij Hint: it may help you write the model cleanly if you define constants for the input data. For example, be the income stream from project i = {A, B, C} at the start of quarter je [n], where points) = 6. QBUS6820 2023 Semeste 1924 or the amount earned (positive n Please refer to the Jupyter Notebook for this question. Implement the model in Gurobi. sure that the model can take into account data of different sizes. meste 3. own a property development firm. You consider investing in three development projects, each of which will take 1.5 years, or six quarters, to complete. For each project, each quarter marks a completion milestone, which may incur costs (e.g., from buying building materials and paying wages) or generate income (e.g., if completed parts of the project are sold to buyers). The table below shows the projected cash flow stream for each project across the six Semester 1 S682 Fa2406 47 You Q4 Q5 820 -1.8 0.4 1.8 1.8 Q6 1.5 1.5 1.5 -1.8 column shows the amount that must be paid (negative numb 92406 1 2023 Leto2 s numbers) for each project at the start of the corresponding quarter, in units of millions of dollars. The last column shows the estimated value of the projects at the end of quarter 6. (Note: project B has negative value at the end since it is a condition to demolish the development at the end of the 1.5 years. Therefore for an initial investment of $2.5 million over two quarters, the project will earn $4.7 million over four cost $1 million to demolish at the end.) S6 but arters, S680 QBarters. A S6820, (b) 139 B th023 m (6 Q2 Q3 -1 -0.5 -2 This means that cash flows are reduced proportionally. For example, if you were to invest 40% into project A, the cash flow would be -1.2, -0.4, It is possible to invest a fractional amount into each project 6820 Se-0.72, 0.16, 0.72, 0.72, 2.2. However, once y the end of the projects. firm has certain amounts to invest at the start of each quarter, gir 2 action, it stays the same until 479240ou decide on your investment 0230 023 in the following table (in millions). Se which increase in value by 3% per quarter; also paid each quarter. me Make s end 5.5 -1 Q1 Q2 Q3 Q4 Q5 Q6 end 0.5 0.4 0.38 0.36 0.34 0.3 2 can supplement these amounts by borrowing money each quarter at an interest rate of 3.5% per quarter. You have borrowing capacity of $2 million each quarter. Any loan taken out at the start of a quarter must be paid back (including interest) at the end of the quarter. You can also choose to invest money in bonds, onds. Bond investments are 23 Sper in 2406ere is no limit for i ho23 Sesting i 470 our goal is to choose how much to invest in the projects, how much to borrow each quarter, and how much to invest in bonds each quarter in order maximize the net worth of your portfolio at the end of Q6. (a) (14 points) Formulate a linear program to find the optimal investment plan. Solve your linear program (using code from part (b)) and interpret the solution. 6. let Cij Hint: it may help you write the model cleanly if you define constants for the input data. For example, be the income stream from project i = {A, B, C} at the start of quarter je [n], where points) = 6. QBUS6820 2023 Semeste 1924 or the amount earned (positive n Please refer to the Jupyter Notebook for this question. Implement the model in Gurobi. sure that the model can take into account data of different sizes. meste

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