The monthly cost for a company that sells designer shoes is given by
$C = 3800 + 20x + 0.7x^2$,
where $C$ is the cost, in USD, when $x$ pairs of shoes are sold each month. If the number of pairs of shoes sold is increasing at a rate of 70 per month, find the rate at which the company's cost is changing with respect to time when 1050 are sold each month. In other words, find $\frac{dC}{dt}$ if we know that $\frac{dx}{dt} = 70$ pairs per month and $x = 1050$ pairs.
$\frac{dC}{dt} = \boxed{} \text{ USD per month}$
