Posted by Roland on .
A company manufactures widgets. The daily marginal cost to produce x widgets is found to be
C'(x) = 0.000009x^2  0.009x + 8
(measured in dollars per unit). The daily fixed costs are found to be $120.
a. Use this information to get a general cost function for producing widgets.
b. Find the total cost of producing the first 500 widgets.
c. If you sell the widgets for $25 each, how many will need to be sold before the company begins making a profit? (Hint: The revenue function is R(x) = $25x;
after you integrate C’(x), set C(x) = R(x) and solve for x. Finding the
intersection of the graphs of these two function may help you here.)

Calculus 
Damon,
c = 9*10^6 x^3/3  9*10^3 x^2/2 + 8 x + constant which is 120 so
c = 3 *10^6 x^3 4.5*10^3 x^2 + 8 x + 120
if x = 5*10^2
go ahead, plug that in
then for break even
25 x = = 3 *10^6 x^3 4.5*10^3 x^2 + 8 x + 120
or
0 = 3*10^6 x^3 4.5*10^3 x  17 x +120 
Calculus 
Damon,
Using an online roots calculator I get x = 3243.358, 1750.404, 7.046
so perhaps 7
check my arithmetic!