Answer:
The marginal cost at the given production level is $49.9.
Step-by-step explanation:
The marginal cost function is expressed as the first derivative of the total cost function with respect to quantity (x).
We have that the cost function is given by
[tex]C(x) = 15000 + 50x + \frac{1000}{x}[/tex]
So, we need the derivative and then we’ll need to compute the value x = 100 of the derivative.
[tex]C'(x)=\frac{d}{dx}\left(15000+50x+\frac{1000}{x}\right)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\C'(x)=\frac{d}{dx}\left(15000\right)+\frac{d}{dx}\left(50x\right)+\frac{d}{dx}\left(\frac{1000}{x}\right)\\\\C'(x)=0+50-\frac{1000}{x^2}\\\\C'(x)=50-\frac{1000}{x^2}[/tex]
When x = 100, the marginal cost is
[tex]C'(100)=-\frac{1000}{100^2}+50\\\\C'(100)=\frac{499}{10}=49.9[/tex]
