The Trusty Investment helps its customers in financial assets planning, whose finance manager is required to prepare a 5-year investment plan with a total amount of $280,000. Trusty has three categories of investment: Mortgage, Commercial Loans, and Bonds, of which each has a different unit cost, and the expected return listed in Table 3. For example, Mortgage A's annual return rate is 11 percent with 4-year maturity, and if the company decides to investment in Mortgage A, the investment will be made at the beginning of year 1, correspondingly the return of Mortgage A will be achieved annually from year 2 to year 5. Compared with Mortgage, however, Commercial Loans provide a lower return rate with shorter year of maturity as well, which provides more flexibility in the assets planning. الم ܒܨ11 ܒܨ1 ܒ10 Investment Choice Unit Cost ($) Return (%) Years of Buying Year Maturity Mortgage AS 2,200 44 Mortgage B2 3,000 104 32 2 Commercial loans 1,500 92 24 34 iBond 1,000 2.32 1,2,3,4 Table 3. Three types of investments Asides from Mortgage & Commercial loans, the corporate also decides to set aside certain amount of liquid money and put in iBond which can be bought annually. Since iBond will mature in one year, the entire principal in the Bond investment can be taken out the next year as needed. The bond generates annual return rate at 2.3 percent. The company decides to put on iBond at the beginning of year 1, year 2, year 3, and year 4 only, excluding year 5. The manager is also required to consider certain conditions stated as follows: In year 1, 2, 3, the investment amount to iBond is at least 25% of the total investment amount. The total investment amount in Mortgage A should be no more than half of the total investment amount. At least 30% of the total investment amount must be allocated to Commercial Loans. Only one of Mortgage A or Mortgage B will be chosen. For investment in Mortgage, at most one unit will be invested. a) Formulate a linear programming model to maximize the total return.