Solve the problem.
-The daily profit in dollars made by an automobile manufacturer is $P ( x ) = - 30 x ^ { 2 } + 1,560 x - 1,470$ where x is the number of cars produced per shift. Find the maximum possible daily profit.
A) $17,305
B) $20,315
C) $18,810
D) $15,989

Question

Quizplus · Accepted Answer

The maximum possible daily profit can be found by using the vertex formula for a quadratic equation $P(x) = ax^2 + bx + c$, where the x-coordinate of the vertex (which gives the number of cars for maximum profit) is given by $-\frac{b}{2a}$. In this case, $a = -30$, $b = 1560$, and $c = -1470$. Plugging these values into the formula gives the x-coordinate as $-\frac{1560}{2(-30)} = 26$. To find the maximum profit (the y-coordinate of the vertex), we substitute $x = 26$ back into the profit equation: $P(26) = -30(26)^2 + 1560(26) - 1470$, which calculates to $18,810.

Solve the Problem P(x)=−30x2+1,560x−1,470P ( x ) = - 30 x ^ { 2 } + 1,560 x - 1,470P(x)=−30x2+1,560x−1,470

Solve the Problem $P ( x ) = - 30 x ^ { 2 } + 1,560 x - 1,470$