A Bank is developing a loan policy of $ 10 million, for the allocation of capital as follows:

Type of loan	Interest Rate	% of debt not paid
Personal	0.15	0.1
Automobile	0.14	0.07
House	0.13	0.01
Agricultural	0.125	0.05
Commercial	0.11	0.02

Unpaid debts are not recovered and do not produce interest income. To compete with other banks the bank needs to allocate a minimum of 40% of the funds to agricultural and commercial loans. To help the construction industry in your region, home loans must represent a minimum of 30% of all your loans. Also, the bank has an explicit policy that does not allow the general ratio of bad loans among all loans to be greater than or equal to 4%.

a) What is the loan designation to maximize the bank's profit? What is its maximum utility?