$(10)[$Marks: $4]$ A manufacturer of belts finds that the total cost $C(x)($in dollars$)$ of manufacturing $x$ belts per day is given by $C(x)=400+4x+0\mathrm{.}0001x^2.$ Each belt can be sold at a price of $p$ dollars, where $p$ is related to $x$ by the demand equation $p=10-0\mathrm{.}0004x.$

If all belts that are manufactured can be sold, what is the largest profit that can be attained? $($Note: Your answer should be in dollars!$).$

$(9)[$Marks: $6]$ The weekly supply of shoes at the given price of $p$ dollars is given by

$p-\frac{1}{2}{q}^2=48$

How fast is the weekly supply of shoes changing when $6$ shoes per week are supplied at a price of $$66,$ and the price is decreasing at the rate of $$3$ per week?