hey guys could you please help me with this problem ? its my h.w and i dont know how to slove it :$
(Bank Loan Policy) A financial institution, the Thriftem Bank, is in the process of formulating a loan policy involving a total of $12 million. Being a full-service faculty, the bank is obligated to grant loans to different clientele. The following table provides the types of loans, the interest rate charged by the bank, and the probability of bad debt at estimated from past experience:
Type of Loan | Interest Rate | Bad Debt
Personal | .140 | .10
Car | .130 | .07
Home | .120 | .03
Farm | .125 | .05
Commercial | .100 | .02
Bad debts are assumed unrecoverable and hence produce no interest revenue.
Competition with other financial institutions in area requires that the bank allocate at least 40% of the total funds to farm and commercial loans. To assist the housing industry in the region, home loans must equal at least 50% of the personal, car, and home loans. The bank also has a stated policy specifying that the overall ratio for bad debts on all loans may not exceed .04.
The objective of the Thriftem Bank is to maximize its net return comprised of the difference between the revenue from interest and lost funds due to bad debts.