Bob owns a watch repair shop. He has found that the cost of operating his shop is given by $c ( x ) = 2 x ^ { 2 } - 156 x + 88$ , 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) 88 watches
C) 20 watches
D) 39 watches

Question

Quizplus · Accepted Answer

The lowest cost occurs at the vertex of the parabola represented by the cost function $c(x) = 2x^2 - 156x + 88$. The x-coordinate of the vertex can be found using the formula $-\frac{b}{2a}$, where $a = 2$ and $b = -156$. Plugging these values in gives $-\frac{-156}{2*2} = 39$, indicating that the lowest cost occurs when Bob repairs 39 watches.

Bob Owns a Watch Repair Shop c(x)=2x2−156x+88c ( x ) = 2 x ^ { 2 } - 156 x + 88c(x)=2x2−156x+88

Bob Owns a Watch Repair Shop $c ( x ) = 2 x ^ { 2 } - 156 x + 88$