The weekly demand for soda is modeled by the function $D(x)=\frac{32\mathrm{.}7}{x^{6711}}$ where the price is in dollars and $x$ is the number of units sold. The canning company will supply $x$ cans when the price is $S(x)=0\mathrm{.}0001x^2$ dollars.

Show all work in determining each of the following:

Determine the quantity and price at the market equilibrium point.

Determine the consumer's surplus.

Determine the producer's surplus.