Question 1196250
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Note that the conditions of the problem make for a quick and easy solution, without any algebra and without any graphing.<br>
(1) The total amount of the loans is a fixed amount;
(2) The rate of return on the auto loans is greater than the rate of return on the home loans;
(3) The rate of return on all the loans together is to be maximized; and
(4) The amount of home loans is to be AT LEAST 4 times the amount of auto loans.<br>
Logical reasoning then tells us that, because the rate of return on the auto loans is higher than on the home loans, we want the largest possible fraction of the total to be auto loans; and that means the fraction of home loans should be as small as possible.  Then, with the amount of home loans being as small as possible and at the same time AT LEAST 4 times the amount of auto loans, the amount of home loans must be EXACTLY 4 times the amount of auto loans.<br>
Simple arithmetic then tells us that, with a total of N$20 million, N$4 million should be made to auto loans and N$16 million should be made to home loans.<br>
ANSWER: N$16 million in home loans and N$4 million in auto loans<br>