Real-life application of Calculus

Hello all,

I am currently doing some real-life applications for calculus and stumbled upon the following question, can anyone please help me?

When a chemical factory produces a certain compound they have observed that the daily amount *y *of defective compounds depends on the total amount *x *that they produce according to the empirical formula:

*y *= 0*.*02*x *+ 0*.*00005*x^*2

where *x *and *y *are measured in kilograms. The manufacturer earns $100 per kilogram of nondefective compound and incurs a loss of $20 per kilogram of defective compound.

(a) Write down a function for the total profit *P*(*x*).

(b) How many kilograms should they produce to maximise their profits?

Any help is much appreciated,

Dranalion