Function replacement:

L(x)=x(P-C(x))

X= 1600- 16P minus P= 100-x/ 16.

Then simplify, that is, 1 topic;

By the way, explain the definition domain;

L(x) takes the derivative of x and solves the stagnation point of x=0.

Substitute the abscissa xi of each stagnation point into the function to find L(xi).

Then the abscissa x 1, x2 of the function endpoint is also substituted to solve f(x 1), f(x2).

Compare the values of each function,

The maximum function value is the maximum profit,

And the corresponding x is the maximum profit output.