2 A bank is attempting to determine where its assets should

2) A bank is attempting to determine where its assets should be invested during the current year. At present, $500,000 is available for investment in bonds, home loans, auto loans, and personal loans. The annual rate of return on each type of investment is known to be:

10% for bonds

16% for home loans

13% for auto loans

20% for personal loans

To ensure that the bank\'s portfolio is not too risky, the bank\'s investment manager has placed the following three restrictions on the bank\'s portfolio:

(a) the amount invested in personal loans cannot exceed the amount invested in bonds.

(b) the amount invested in home loans cannot exceed the amount invested in auto loans.

(c ) no more than 25% of the total amount invested may be in personal loans.

The banks objective is to maximize the annual return on the investment portfolio. Formulate the LP that could be solved to meet this goal, as well as briefly describe each variable/constraint.   You do NOT need to solve.

VARIABLES

OBJECTIVE

CONSTRAINTS

Solution

Ans) Variable

         Let X1 : Dollars invested in bonds

         Let X2 : Dollars invested in home loans

         Let X3 : Dollars invested in auto loans

         Let X4 : Dollars invested in personal loans

         Objective

         Max Z = 0.10X1 + 0.16X2 + 0.13X3 + 0.20X4

         Constraints

          X1 + X2 + X3 + X4                                   <= 50000

         -X1         +          X4                                   <= 0

          X2         -           X3                                   <= 0          

         -0.25X1 - 0.25X2 - 0.25X3 + 0.75X4         <= 0

          X1 , X2 , X3 , X4                                       =>0