Question

Bank provides 5 different loans. The types of these loans and monthly interest rates are given below.

Type Of Credit Percentage Of Interest(month)

A (commercial)                                5.5

B)(home)                                          3.5

C (auto)                                             5

D (House 2)                                       4.5

E (short term))                                  6

The bank can give credit £ 100 million. The goal is to maximize interest income

But have some obligations about the loans:

Credit C cannot be more than 25% of credit B.

Credit A can be given up to a maximum of credit D.

The bank must give at least 50% of its loans from types B and D.

Credit B must be at least 1.5 times that of credit D.

The type E Loan cannot exceed 10 million £.

Create a mathematical programming model that will find the optimal credit distribution plan of the bank. Prepare this model in Excel and obtain the optimal plan.

Answer 1

Let us consider

A be the Commercial lone

B is the home loan

C is the auto loan

D is the house 2 loan

E is the short term loan

Given The bank can give credit £ 100 million.

A+B+C+D+E=£ 100 million.

Credit C cannot be more than 25% of credit B.

C<=0.25B

Credit A can be given up to a maximum of credit D.

A<=D

The bank must give at least 50% of its loans from types B and D

B+D>= 50% Of £ 100 million.

B+D =£ 50 million.

Credit B must be at least 1.5 times that of credit D.

B.>=1.5 D

The type E Loan cannot exceed 10 million £.

E<=£ 10 million.

Here the Optimum credit distribution for Profit maximization is to give loan for HOME (B) that 100% amount, The Profit obtained will be 3.5 million euros.