Solve the problem.
-The daily profit in dollars of a specialty cake shop is described by the function $P ( x ) = - 3 x ^ { 2 } + 168 x - 1920$, where $x$ is the number of cakes prepared in one day. The maximum profit for the company occurs at the vertex of the parabola. How many cakes should be prepared per day in order to maximize profit?
A) 28 cakes
B) 2352 cakes
C) 784 cakes
D) 56 cakes

Question

Quizplus · Accepted Answer

The vertex of a parabola given by $P(x) = ax^2 + bx + c$ can be found using the formula $x = -\frac{b}{2a}$. For the given function $P(x) = -3x^2 + 168x - 1920$, $a = -3$ and $b = 168$. Plugging these values into the formula gives $x = -\frac{168}{2(-3)} = 28$. Therefore, to maximize profit, 28 cakes should be prepared per day.

Solve the Problem P(x)=−3x2+168x−1920P ( x ) = - 3 x ^ { 2 } + 168 x - 1920P(x)=−3x2+168x−1920

Solve the Problem $P ( x ) = - 3 x ^ { 2 } + 168 x - 1920$