Bob owns a watch repair shop. He has found that the cost of operating his shop is given by $c ( x ) = 4 x ^ { 2 } - 288 x + 50$ where x is the number of watches repaired. How many watches must he repair to have the lowest cost?
A) 50 watches
B) 36 watches
C) 25 watches
D) 40 watches

Question

Quizplus · Accepted Answer

The cost function $c(x) = 4x^2 - 288x + 50$ is a quadratic equation where the coefficient of $x^2$ is positive, indicating a parabola that opens upwards. The vertex of this parabola gives the minimum cost. The x-coordinate of the vertex can be found using the formula $-\frac{b}{2a}$, where $a = 4$ and $b = -288$. Plugging these values in gives $-\frac{-288}{2*4} = 36$, meaning Bob must repair 36 watches to have the lowest cost.

Bob Owns a Watch Repair Shop c(x)=4x2−288x+50c ( x ) = 4 x ^ { 2 } - 288 x + 50c(x)=4x2−288x+50

Bob Owns a Watch Repair Shop $c ( x ) = 4 x ^ { 2 } - 288 x + 50$