Answer:
80 000
Explanation:
Let the amount in dollars be given as:
[tex]C(x) =576 000 + 160 x + 0.001x^{2}[/tex]
The minimum number of devices is given by differentiating the expression like this:
let C(x) = y
Therefore:
[tex]\frac{dy}{dx} = \frac{d}{dx}[ 576 000 + 160 x + 0.001x^{2} ]\\= 160 + 0.002 x[/tex]
at the minimum point, [tex]\frac{dy}{dy} = 0[/tex]
Therefore,
[tex]160 + 0.002 x = 0[/tex]
solving for x:
[tex]0.002x = 160\\ x = 80 000[/tex]
So, 80 000 units have to be manufactured.
