Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The daily profit in dollars made by an automobile manufacturer is $P ( x ) = - 40 x ^ { 2 } + 2,240 x - 17,000$ where x is the number of cars produced per shift. Find the maximum possible daily profit.
A) $13,211
B) $14,360
C) $31,360
D) $13,642

Question

Quizplus · Accepted Answer

The maximum possible daily profit can be found by using the vertex formula for a parabola given by $P(x) = ax^2 + bx + c$. The x-coordinate of the vertex, which gives the number of cars produced for maximum profit, is found using $-\frac{b}{2a}$. Here, $a = -40$ and $b = 2240$, so $-\frac{2240}{2(-40)} = 28$. Plugging $x = 28$ back into the profit equation gives the maximum profit: $P(28) = -40(28)^2 + 2240(28) - 17000 = 14360$.

Write the Word or Phrase That Best Completes Each Statement P(x)=−40x2+2,240x−17,000P ( x ) = - 40 x ^ { 2 } + 2,240 x - 17,000P(x)=−40x2+2,240x−17,000

Write the Word or Phrase That Best Completes Each Statement $P ( x ) = - 40 x ^ { 2 } + 2,240 x - 17,000$