Palmetto national savings and loan makes five kinds of loans

FINANCE (BANKING)

Palmetto National Savings and Loan makes five kinds of loans. These loans, with the yearly interest rate charged to customers, are shown in the table below:

Type of Loan Interest charges (percent)
Commercial loans 15
Home mortgage (first mortgage) 10
Home improvements 13.6
Home mortgage (second mortgage) 14
Short-term revolving loan 18 

The bank has $53 million in available funds. Its objective is to maximize yield on investment.

The Demand for Funds

The demand for short-term revolving loans never exceeds $5
million. All other demands are unlimited.

Policies and Regulations

a. Home improvement loans cannot be higher than 20 percent of first mortgage loans.
b. Commercial loans must be smaller than or equal to the second mortgage loans.
c. The bank must invest at least 60 percent of the loans outstanding (total loans) in mortgages.
d. For safety reasons, there must be at least $2 invested in first mortgage loans for every dollar invested in second mortgage loans.
e. Short-term loans cannot exceed $5 million.

Find the best bank fund allocation plan.

AUDITING

Arthur and Son, P.A., is an auditing firm that conducts both financial and operational audits. Arthur can conduct 90 financial audits (FAs) per year if he spends full time on just FAs, or 180
operational audits (OAs) per year full time, or any linear combination of both. Son processes the reports made by Arthur. Son can prepare 180 financial audit reports or 150 operational audit reports per year, or any linear combination thereof. The office staff finalizes the reports  submitted by Son. They can handle no more than 160 reports of any kind, per year. Arthur and Son have calculated that to keep their association solvent, they must produce at least 30 FAs and 50 OAs each year. The profit from each FA has averaged $720 in the past and for each OA has been about $650. How many FAs and OAs should Arthur and Son attempt to conduct each year to maximize their firm’s profits?