A garden shop determines the demand function $q=D(x)=\frac{2x+200}{10x+11}$ during early summer for tomato plants where $q$ is the number of plants sold per day when the price is $x$ dollars per plant.
(a) Find the elasticity.
(b) Find the elasticity when $x=2$.
(c) At $\mathrm{\$}2$ per plant, will a small increase in price cause the total revenue to increase or decrease?
(a) The elasticity is

Step 1 ：Given the demand function $q=D(x)=\frac{2x+200}{10x+11}$, where $q$ is the number of plants sold per day when the price is $x$ dollars per plant.

Step 2 ：The elasticity of demand is a measure of how much the quantity demanded of a good responds to a change in the price of that good. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.

Step 3 ：In this case, the elasticity of demand can be calculated using the formula: Elasticity = $(dq/dx)\ast (x/q)$, where $dq/dx$ is the derivative of the demand function with respect to $x$, $x$ is the price, and $q$ is the quantity demanded.

Step 4 ：First, we calculate the derivative of the demand function with respect to $x$: $dq/dx=-10\ast (2\ast x+200)/(10\ast x+11{)}^2+2/(10\ast x+11)$.

Step 5 ：Then, we substitute the values of $x$, $q$, and $dq/dx$ into the elasticity formula to get the elasticity of the demand function: $x\ast (10\ast x+11)\ast (-10\ast (2\ast x+200)/(10\ast x+11{)}^2+2/(10\ast x+11))/(2\ast x+200)$.

Step 6 ：Final Answer: The elasticity of the demand function is given by $\boxed{{\displaystyle x\cdot \frac{(10x+11)\cdot (-10\cdot \frac{(2x+200)}{(10x+11{)}^2}+\frac{2}{10x+11})}{2x+200}}}$