I am new to matrices so I might be wrong.
Firstly we multiply a and b. For the first element (the top one on a) we multiply that by every single element in b, then we do that for the second element in a, then for the third, hence we get.
Then we add all this up to give us 198.
Next we do the same process except for b. Thus,
Then we add all that up to get 770. So as of right now we have 770 + 198.
Next we do the same process for a again but to c, hence we get
Now, we have 198+770+315, which gives us 1283.
I am most likely wrong :).
Sorry I am not 100% how to explain this but basically by completing the square, we can eventually put the equation in vertex form, which in this case will give us the maximum. In this the equation became -1(x+27.5)^2+765.25. So we know that 765.25 is the maximum.
Essentially, we just complete the square so we can easily fine the vertex through vertex form.
I will admit I have done this a few times, but i am mostly looking for the steps, I really don't care if I get 5/7 or a 3/7, I only want to learn the content, and sometimes teh message boards dont help. I think thats why many kids come here including myself sometimes come here to ask for help, while others only want answers. I understand your point, maybe people could ask for starting points instead of direct answers?
For the maximum, I started off by adding up all the integers. 1+2+3...+10=55.
So with that I gave a variable to each group, x and y.
Thus, x+y=55, then I switched that to a slope intercept form, so y= -x+55
So that gave me P= y * x, which I then simplified to P= x* (-x+55), which became -(x^2-55x)
Then we can complete the square to get -(x^2-55x+765.25), and that simplified is -(x-27.5), so 27.5* 27.5 will give us the highest number, but since we only have intergers we can go +1 and -1 to get 27*28 and that will equal 756.