a liquid form of penicillin is sold in bulk at a price of $ 200 per unit.If the total cost for x unit is C(x)=500000+80x+0.003X^2 and the production capacity is at most 30000 at a specified timed, how many of the penicillin must be manufactured and sold in that time to maximize profit?

Answer 1

profit = selling price - cost of making it
=200x - 500000 - 80x - .0003x^2
d(profit) = 120 - .006x
= 0 for a max of profit
x = 120/.006 = appr. 120

check:
at x = 119 , profit = clearly negative
this question makes no sense to me
What is that huge number in C(x) supposed to represent?

Answer 2

x = 120/.006 = 20000

check:
let x = 19000, profit = 697000
let x = 20000, profit = 700000
let x = 21000, profit = 697000

the maximum number they should manufacture is
20000