Posted by **Yuni** on Wednesday, July 27, 2011 at 7:02am.

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?

- math -
**Reiny**, Wednesday, July 27, 2011 at 8:43am
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?

- my type error - math -
**Reiny**, Wednesday, July 27, 2011 at 8:49am
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

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