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 (%, percent)

Commercial Loans                                           8

Home Mortgages                                  4

Home Improvements                              6

Short-term revolving loans                     10

The bank has $25 million in available funds. Its objective is to maximize yield on investment. The demand for short-term revolving loans never exceeds $10 million. Also there are policies and regulations on loans:

a.    Home improvement loans cannot be higher than 40 percent of home mortgage loans.

b.    Commercial loans cannot be higher than 20 percent of the home mortgage loans.

c.    The bank must invest at least 50 percent of the loans outstanding (total loans) in mortgages.

Formulate this problem as an LP.

Answer 1

		Commercial loans	Home mortgages	Home Improvements	ST Loans
	Amount loaned	2,500,000.00	12,500,000.00	-	10,000,000.00
	Interest	8%	4%	6%	10%
MAXIMIZE	Total Interest	1,700,000.00
CONSTRAINTS
1	TOTAL FUNDS	25,000,000.00	<=	25,000,000.00
2	short-term revolving loans	10,000,000.00	<=	10,000,000.00
3	Home improvement loans cannot be higher than 40 percent of home mortgage loans.	-	<=	5,000,000.00
4	Commercial loans cannot be higher than 20 percent of the home mortgage loans	2,500,000.00	<=	2,500,000.00
5	at least 50 percent of the loans outstanding (total loans) in mortgages.	12,500,000.00	>=	12,500,000.00

PROBLEM IN EXCEL LP