Exercise of mathematical function in senior one.

First, trim the function for this function.

First, multiply both sides by -50 to get it.

-50y = x2-8 100 x+ 1050000

Then match the box program on the left to get it.

-50y = x2-8 100 x+ 16402500- 16402500+ 1050000

Get it after completion

-50y =(x-4050)2- 16402500+ 1050000

After further sorting, we get.

50y= 15352500-(x-4050)2

Because the square of (x-4050) is nonnegative, this function has a maximum only when X=4050.

Therefore, when X=4050, the monthly income of the leasing company is the largest.

At this time Y= 15352500/50=307050.

So the highest monthly income is 307,050 yuan.

All the above are calculated by hand.