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 amountyof defective compounds depends on the total amountxthat they produce according to the empirical formula:

y= 0.02x+ 0.00005x^2

wherexandyare 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 profitP(x).

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

Any help is much appreciated,

Dranalion