Valley National Bank has $1 million in funds to be allocated between home loans, personal loans and auto loans. The annual rates of return for the loans are 7% for home loans, 12% for personal loans and 9% for auto loans. The bank's planning committee has decided that at least 40% of the funds be allocated to home loans. In addition, the planning committee has determined that the amount allocated to personal loans cannot exceed 60% of the amount allocated to auto loans. a. Formulate the problem as a linear programming model including decision variables, objective function and the constraints.
b. What is the optimal allocation of funds ($) for Valley National Bank and the projected return ($)?
c. If the interest rates on home loans increased to 9% - use the output from sensitivity analysis (ie do not just re-run the program) to calculate what the allocated funds ($) will be and what the total return will be ($).
d. Suppose the amount of funds available for investment increased by $10,000, use the sensitivity report and the shadow price to calculate the change on the solution and the profit (one decimal place).
e. Assume that Valley National Bank has the original $1 million in funds available and that the planning committee agreed to relax the requirement that at least 40% of the new funds must be allocated to home loans by 1%. Use the shadow price as quoted on the report. What is the shadow price (4 decimals)? What would the new allocation be and what would the change be on the projected return?
f. If the return on home loans increased by 1% and the return on personal loans decreased by 1%,use the 100% rule to explain if the following change is allowable. What is the % rule value (2 decimal places)?
g. If the return on home loans increased by 1% and the return on personal loans decreased by 1%,use the 100% rule to explain if the following change is allowable. What is the new return?