Bob owns a watch repair shop. He has found that the cost of operating his shop is given by $c(x)=2 x^{2}-148 x+85$, where $x$ is the number of watches repaired. How many watches must he repair to have the lowest cost?
A) 20 watches
B) 42 watches
C) 85 watches
D) 37 watches

Question

Quizplus · Accepted Answer

The cost function $c(x)=2x^2-148x+85$ is a quadratic function, and its graph is a parabola opening upwards. The vertex of this parabola gives the minimum cost. The x-coordinate of the vertex is given by $-b/(2a)$, where $a=2$ and $b=-148$. Calculating this gives $x=37$.

Bob Owns a Watch Repair Shop c(x)=2x2−148x+85c(x)=2 x^{2}-148 x+85c(x)=2x2−148x+85 , Where xxx

Bob Owns a Watch Repair Shop $c(x)=2 x^{2}-148 x+85$ , Where $x$