Someone else asked the same question but copied the whole thing from the CFA text so it got taken down by the moderator, but my explanation is below (if its a little confusing let me know… My lack of ability to explain things properly is probably one of the key reasons I am resitting level 3):
The first portfolio will need to be invested in 100% riskless assets as the client will not accept any loss.
For the second you need to work out the expected return for each level. Riskless is easy as it is 1%, when you calculate layer 2 (moderately risky investments) you will find the return is 4.6% (-.03*.1 + .05*.8 + .09*.1), which is below the return objective. Knowing that you need to achieve 5% you can eliminate this layer. Next you work out layer 3 return (the risky layer) which works out at 24.75% (same math as before).
With the above you know you can work this out from the riskless and risky layers. Remember that there is a possibility that you could lose 50% of the value with layer three so your split between layers 1 and 3 needs to work so that initial investment is (layer 1*1.01 + layer 3 *.5) = 1,800,000 remembering layer 3 will equal (2,000,000-layer 1). Once you have substituted this in you should get (layer 1*1.01)+((2,000,000-layer 1)*.5) = 1,800,000, which you can rearrange to get the amount required for layer 1 and then 2,000,000- layer 1 amount will give you layer 3.
(x*1.01)+((2,000,000-x)*.5)=1,800,000
(x*1.01)+(1,000,000-.5x)=1,800,000
x*1.01-.5x=800,000
.51x=800,000
x=1,568,627