Caribbean Commercial Bank (CCB) has $1 million in new funds that must be allocated to home loans, personal loans, and automobile loans. The annual rates of return of the three types of loans are 7% for home loans, 12% for personal loans, and 9% for automobile loans. The banks planning committee has decided that at least 40% of the new funds must be allocated to home loans. In addition, the planning committee has specified that the amount allocated to personal loans cannot exceed 60% of the amount allocated to automobile loans.

(a) Formulate a linear programming model that can be used to determine the amount of funds CCB should allocate to each type of loan in order to maximize the total annual return for the new funds. (5marks)

The banks financial analyst provides EXHIBIT 1 (page 9) which details The Management Scientist 6.0 computer output of the optimal solution to the correctly formulated Linear programming model in (a): Using the information from the Computer output in Appendices 1 & 2:

(b) How much should be allocated to each type of loan? (3 marks)

(c) What is the total annual return? What is the percentage annual return?

(2 marks) (d) If the interest rate on home loans increased to 9%, would the amount allocated to each type of loan change? Explain. (3 m