SKILL CHECK

$($this one is very similar to a homework problem$)$

A bank has $1$ million dollars available for the next year to distribute to people seeking loans. With every type of loan, there is always a small percentage of loans that end up in default. For these, neither the principal nor the interest can be recovered. These are called bad debts. For the next year, the interest rates for each type of loan, as well as the expected percentage of bad debts, are given in the following table:

$\backslash$table$[[$Type of Loan,Interest rate,$\%$ Bad Debts$],[$Personal$,0\mathrm{.}052,11],[$Car$,0\mathrm{.}07,7],[$Home$,0\mathrm{.}076,1\mathrm{.}5],[$Business$,0\mathrm{.}13,3]]$

The bank must allocate at least $30\%$ of their loans to home and business, while car loans must equal no more than $40\%$ of the total loans given out for personal purposes, homes, and businesses combined. Finally, no more than $3\%$ of all the money loaned out can go to bad debts. How much money must be loaned out in each loan type so that the bank can maximize their annual return from these loans?