The financial manager of Dukes, Inc., is charged with managing the company's cash flow. She must manage short-term investments to maximize cash value at the end of the time horizon, while making sure that funds are available to pay company expenditures. She is considering three investment options over the next four months: (1) Investment A, matures in one month, is available at the beginning of each month, and pays 0.5%; (2) Investment B, matures in 3 months, is available at the beginning of each month, and pays 2.1%; and (3) C, a 4-month CD that is available only at the beginning of month 1 and pays 3,5%. The company currently has $300,000 in cash. The expected cash inflows and outflows over the next four months, starting with month 1, are as follows: ($50,000), $12,000, ($23,000), $20,000. (Note that dollar amounts in parenthesis indicate a net outflow of cash (for example, at the start of the month 1, $50,000 will be paid out of the company accounts). Dollar amounts without parenthesis indicate a net cash inflow (at the start of month 2, $12,000 will be added to the company accounts).] In addition, the firm wants the weighted average risk level during months 2 and 4 to be no more than 5 (for each month). The risk ratings are 3 for investment A, 6 for investment B, and 4 for investment C. You are provided the following variables: A: = amount invested in A at the beginning of month i = 1, 2, 3, 4 B = amount invested in B at the beginning of month j = 1, 2 C = amount invested in C at the beginning of month 1 Formulate only the following parts of the LP model. Use the decision variables provided. NO credit if you make up new variables! Write the question # and your answer. 1. Write the objective function. 2. Write the constraint for the beginning of month 1. 3. Write the constraint for the beginning of month 4. 4. Write the risk constraint for month 2. The financial manager of Dukes, Inc., is charged with managing the company's cash flow. She must manage short-term investments to maximize cash value at the end of the time horizon, while making sure that funds are available to pay company expenditures. She is considering three investment options over the next four months: (1) Investment A, matures in one month, is available at the beginning of each month, and pays 0.5%; (2) Investment B, matures in 3 months, is available at the beginning of each month, and pays 2.1%; and (3) C, a 4-month CD that is available only at the beginning of month 1 and pays 3,5%. The company currently has $300,000 in cash. The expected cash inflows and outflows over the next four months, starting with month 1, are as follows: ($50,000), $12,000, ($23,000), $20,000. (Note that dollar amounts in parenthesis indicate a net outflow of cash (for example, at the start of the month 1, $50,000 will be paid out of the company accounts). Dollar amounts without parenthesis indicate a net cash inflow (at the start of month 2, $12,000 will be added to the company accounts).] In addition, the firm wants the weighted average risk level during months 2 and 4 to be no more than 5 (for each month). The risk ratings are 3 for investment A, 6 for investment B, and 4 for investment C. You are provided the following variables: A: = amount invested in A at the beginning of month i = 1, 2, 3, 4 B = amount invested in B at the beginning of month j = 1, 2 C = amount invested in C at the beginning of month 1 Formulate only the following parts of the LP model. Use the decision variables provided. NO credit if you make up new variables! Write the question # and your answer. 1. Write the objective function. 2. Write the constraint for the beginning of month 1. 3. Write the constraint for the beginning of month 4. 4. Write the risk constraint for month 2