Question

A fertilizer producer finds that it can sell its product at a price of p=300-x dollars per unit
when it produces x units of fertilizer. The total production cost (in dollars) for x units is
C(x)= 20,000+24x+0.5x^2. How many units must be manufactured to maximize the profit?

Answer 1

find the max of

f(x) = x*p(x)-c(x)
= x(300-x)-(20000+24x+1/2 x^2)
= -3/2 x^2 + 276x - 20000

f' = -3x + 276
f'=0 at x=92
since f" < 0, that is a max.

Answer 2

thank you