Question

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.)

Answer 1

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

Answer 2

Using an online roots calculator I get x = 3243.358, -1750.404, 7.046

so perhaps 7
check my arithmetic!