Provide an improved or generalized version of the MODEL in AMPL (eg additional types of loans can be added and total amounts of loan in relation to the total fund can be changed according to preference)

OBJECTIVE:

maximize the net return of the Bank in the area of interest from loans such as Personal loan, Car loan, Home loan, Agricultural loan, Commercial loan, Education loan

ASSUMPTION FOR PROBLEM (a) It is assumed that the total loan amount of Bank for maximum profit is fixed. (b) It is assumed that the total amount for investing for maximum profit is fixed. (c) It is assumed that there is a linear relationship among the variables used in the problem.

The data is below: The total fund is Rs. 150 crore for different loan products. The bank is faced with following constraints:

(a) Amounts allocated to the different loan products not more than the total fund. (b) The total amount for Home loan, Agricultural loan and Educational loan not more than 60% of the total fund. (c) The total amount for Personal loan and Car loan not more than 50% of the total fund. (d) The total amount for Commercial loan (Secured) not more than 40% of the total fund. (e) The total amount for Commercial loan (Unsecured) not more than 20% of the total fund. (f) The total amount allocated to Home Loan is atleast 5% of the total fund. (g) The total amount allocated to Agricultural loan is atleast 5% of the total fund. (h) The total amount allocated to Car loan is atleast 5% of the total fund.

The interest rate of different loans are given in following table: (MCLR = 8.60%)

Types of loan	Rate of Interest
Home	8.60%
Agricultural	8.60%
Car	MCLR + 0.4% = 9.00%
Personal	MCLR + 3% = 11.60%
Educational	MCLR + 2% = 10.60%
Commercial (Secured / Unsecured)	MCLR + 1.5 = 10.10%

MODEL FILE IN AMPL

# DECISION VARIABLES var x1; #Home var x2; #Agricultural var x3; #Car var x4; #Personal var x5; #Educational var x6; #Commercial (Secured) var x7; #Commercial (Unsecured)

# OBJECTIVE FUNCTION maximize Z: 0.086*x1 + 0.086*x2 + 0.09*x3 + 0.116*x4 + 0.106*x5 + 0.101*x6 + 0.101*x7

# CONSTRAINTS s.t. x1 + x2 + x3 + x4 + x5 + x6 + x7 <= 150; s.t. x1 + x2 + x5 <= 90; s.t. x3 + x4 <= 75; s.t. x6 <= 60; s.t. x7 <= 30; s.t. x1 >= 7.5; s.t. x2 >= 7.5; s.t. x3 >= 7.5; s.t. x1 >= 0; s.t. x2 >= 0; s.t. x3 >= 0; s.t. x4 >= 0; s.t. x5 >= 0; s.t. x6 >= 0; s.t. x7 >= 0;

DATA FILE IN AMPL

# PART 1: DECISION VARIABLES var x1 >=0; #Let amount for Home Loan var x2 >=0; #Let amount for Agricultural Loan var x3 >=0; #Let amount for Car Loan var x4 >=0; #Let amount for Personal Loan var x5 >=0; #Let amount for Educational Loan var x6 >=0; #Let amount for Commercial Loan (Secured) var x7 >=0; #Let amount for Commercial Loan (Unsecured)

# PART 2: OBJECTIVE FUNCTION maximize Z: 0.086*x1 + 0.086*x2 + 0.09*x3 + 0.116*x4 + 0.106*x5 + 0.101*x6 + 0.101*x7;

# PART 3: CONSTRAINTS s.t. M1: x1 + x2 + x3 + x4 + x5 + x6 + x7 <= 150; s.t. M2: x1 + x2 + x5 <= 90; s.t. M3: x3 + x4 <= 75; s.t. M4: x6 <= 60; s.t. M5: x7 <= 30; s.t. M6: x1 >= 7.5; s.t. M7: x2 >= 7.5; s.t. M8: x3 >= 7.5; s.t. M9: x1 >= 0; s.t. M10: x2 >= 0; s.t. M11: x3 >= 0; s.t. M12: x4 >= 0; s.t. M13: x5 >= 0; s.t. M14: x6 >= 0; s.t. M15: x7 >= 0;s

ANSWERS IN AMPL: x1 = 7.5 x2 = 7.5 x3 = 7.5 x4 = 67.5 x5 = 60 x6 = 0 x7 = 0 Z = 16.155