Bob owns a watch repair shop. He has found that the cost of operating his shop is given by $c(x)=3 x^{2}-174 x+87$, where $c$ is cost and $x$ is the number of watches repaired. How many watches must he repair to have the lowest cost? A. 44 watches B. 87 watches C. 30 watches D. 29 watches

Step 1 ：The cost function is a quadratic function. The minimum value of a quadratic function \(f(x) = ax^2 + bx + c\) is achieved at \(x = -\frac{b}{2a}\). In this case, \(a = 3\) and \(b = -174\). So, we need to calculate \(x = -\frac{-174}{2*3}\).

Step 2 ：Substitute the values of a and b into the formula, we get \(x = -\frac{-174}{2*3} = 29.0\)

Step 3 ：Final Answer: \(\boxed{29 \text{ watches}}\). The correct answer is D. 29 watches.