Question

A local SME bank provides 4 types of loans of its customers and these loans yield the following interest rates to the Bank:

1. Personal Loan 1:         14%
2. Personal Loan 2:         20%
3. Home Loan:                20%
4. Overdraft:                   10%

The Bank has a maximum foreseeable lending capability of Rs 700 million and is further constrained by the policies:

1. Personal Loan 1 must be at least 45% of all personal loans issued and at least 15% of all loans issued (in Rs terms);
2. Personal Loan 2 cannot exceed 40% of all loans issued (in Rs Terms);
3. To avoid public displeasure and the introduction of a new tax, the average interest rate on all loans must not exceed 10%.

Formulate the Linear Programming Problem.

Note: To maximise interest income whilst satisfying the policy limitations.

Answer 1

ANSWER::

Formulation of the Linear Programming Problem

x1 = personal loan 1 (in Rs)

x2 = personal loan 2 (in Rs)

x3 = home loan (in Rs)

x4 = overdraft (in Rs)

constraints :

x1>=0 , x2>=0 , x3>=0, x4>=0

a)

x1 <= (0.45)*(x1+x2+x3+x4)

x1 >= (0.15)*(x1+x2+x3+x4)

b)

x2 <= (0.40)*(x1+x2+x3+x4)

c)

(14*x1+20*x2+20*x3+10*x4) / (x1+x2+x3+x4) <= 10

maximise : interest income

interest income = (0.14*x1 + 0.20*x2 + 0.20*x3 + 0.10*x4)

(Note : no need to solve the LPP as the question only requires to formulate the LPP)

------------------------------------------------------------------------

DEAR STUDENT,

IF YOU HAVE ANY QUERY ASK ME IN THE COMMENT BOX,I AM HERE TO HELPS YOU.PLEASE GIVE ME POSITIVE RATINGS

*****************THANK YOU***************