The cost to produce $q$ units is modeled by the cost function $C(q)=0.115 q^{2}-46 q+4700$. What quantity of units minimizes the cost of production? a. $q=327$ b. $q=411$ c. $q=200$ d. $q=100$ e. $q=500$

Step 1 ：The cost to produce $q$ units is modeled by the cost function $C(q)=0.115 q^{2}-46 q+4700$.

Step 2 ：We want to find the quantity of units that minimizes the cost of production.

Step 3 ：To find the minimum of a function, we can use the formula for the vertex of a parabola, which is $q = -b/(2a)$, where $a$ and $b$ are the coefficients of the quadratic and linear terms, respectively.

Step 4 ：Substituting the given values, we have $a = 0.115$ and $b = -46$.

Step 5 ：Calculating $q = -b/(2a)$, we get $q = 200$.

Step 6 ：Final Answer: The quantity of units that minimizes the cost of production is \(\boxed{200}\).