Question

Pittsburg Savings & Loan makes four kinds of loans. These loans, with the yearly interest rate charged to

customers, are shown in the table below.

Type of Loan

Interest Charged (in

%, percent

)

Commercial Loans

7

Home Mortgages

4

Home Improvements

6

Short-term revolving loans

8

The bank has $20 million in available funds. Its objective is to maximize yield on investment. The

demand for short-term revolving loans never exceeds $ 3 million. Also there are policies and regulations

on loans:

a.

Home improvement loans cannot be higher than 20 percent of home mortgage loans.

b.

Commercial loans cannot be higher than 30 percent of the home mortgage loans.

c.

The bank must invest at least 40 percent of the loans outstanding (total loans) in mortgages.

Formulate this problem as an LP.

Answer 1

Let the variables be as defined below:

Commercial Loans	a
Home Mortgages	b
Home Improvements	c
Short-term revolving loans	d

The objective function is: Z = 0.07a + 0.04b + 0.06c + 0.08d. This has to be maximized.

Constraints:

(1) a+b+c+d<=20 million

(2) d<=3 million

(3) c<=0.2a

(4) a<=0.3b

(5) b>=0.4(a+b+c+d)

The above can be solved in excel using the solver function. The result is:

	(in $ millions)
Commerical Loans	3.75
Home Mortgages	12.5
Home Improvements	0.75
Short-term revolving loans	3.00
Objective function (Z)	1.0475
Constraints
20	<=	20
3	<=	3
0.750000027	<=	0.75
3.750000084	<=	3.75
12.49999989	>=	8