Obviously, if he were to only maximize his income he would put all money on the higher interest. But to reduce the risk he will balance the investment. He will put a fraction a (between 0 and 1) of the 710000 on 1% and the rest (1-a) on the 4.5%. Both interests together must then satisfy to add up to 18000.
So written as an equation:
[tex]710000\cdot a\cdot 0.01 + 710000\cdot(1-a)\cdot 0.045 = 18000[/tex]
I am not going to solve step by step assuming you can solve for a (if not let me know) but the solution is
[tex]a = 279/497[/tex]
So that means he should put
[tex]710000\cdot \frac{279}{497} \approx 398571[/tex] on the 1% account, and the rest 311429 on the riskier 4.5% account.
