Solve the problem.
-An automobile manufacturer can produce up to 300 cars per day. The profit made from the sale of these vehicles can be modeled by the function $P ( x ) = - 10 x ^ { 2 } + 1,900 x - 34,000$ where P(x) is the
Profit in dollars and x is the number of automobiles made and sold. How many cars should be made
And sold to maximize profit?
A) 1,900
B) 95
C) 45
D) 190

Question

Quizplus · Accepted Answer

To maximize profit, we need to find the vertex of the parabola represented by the given quadratic function $P(x) = -10x^2 + 1,900x - 34,000$. The x-coordinate of the vertex, which gives the number of cars to produce to maximize profit, can be found using the formula $-\frac{b}{2a}$, where $a = -10$ and $b = 1,900$. Plugging these values in gives $-\frac{1,900}{2(-10)} = 95$.

Solve the Problem P(x)=−10x2+1,900x−34,000P ( x ) = - 10 x ^ { 2 } + 1,900 x - 34,000P(x)=−10x2+1,900x−34,000

Solve the Problem $P ( x ) = - 10 x ^ { 2 } + 1,900 x - 34,000$