Solve the problem.
-The monthly profit for a small company that makes long-sleeve T-shirts depends on the price per shirt. If the price is too high, sales will drop. If the price is too low, the revenue brought in may not
Cover the cost to produce the shirts. After months of data collection, the sales team determines that
The monthly profit is approximated by $f ( p ) = - 33 p ^ { 2 } + 1,254 p - 10,763$ , where p is the price per shirt
And f p is the monthly profit based on that price. Find the price that generates the maximum profit
And find the maximum profit.
A) $p = \$ 19$
$f ( p ) = \$ 1,150$

B) $p = \$ 38$
$f ( p ) = \$ 10,763$

C) $p = \$ 19$
$f ( p ) = \$ 24,976$

D) $p = \$ 38$
$f ( p ) = \$ 1,150$

Question

Solve the problem.
-The monthly profit for a small company that makes long-sleeve T-shirts depends on the price per shirt. If the price is too high, sales will drop. If the price is too low, the revenue brought in may not
Cover the cost to produce the shirts. After months of data collection, the sales team determines that
The monthly profit is approximated by $f ( p ) = - 33 p ^ { 2 } + 1,254 p - 10,763$ , where p is the price per shirt
And f p is the monthly profit based on that price. Find the price that generates the maximum profit
And find the maximum profit. 
A) $p = \$ 19$
$f ( p ) = \$ 1,150$

B) $p = \$ 38$
$f ( p ) = \$ 10,763$

C) $p = \$ 19$
$f ( p ) = \$ 24,976$

D) $p = \$ 38$
$f ( p ) = \$ 1,150$

Quizplus · Accepted Answer

The maximum profit is found by determining the vertex of the parabola represented by the profit function $f(p) = -33p^2 + 1,254p - 10,763$. The x-coordinate of the vertex, which gives the price per shirt for maximum profit, is found using the formula $-\frac{b}{2a}$, where $a = -33$ and $b = 1,254$. This calculation gives $p = \frac{1,254}{2 \cdot 33} = 19$. Substituting $p = 19$ into the profit function gives the maximum profit, which is $f(19) = -33(19)^2 + 1,254(19) - 10,763 = \$1,150$.

Solve the Problem f(p)=−33p2+1,254p−10,763f ( p ) = - 33 p ^ { 2 } + 1,254 p - 10,763f(p)=−33p2+1,254p−10,763

Solve the Problem $f ( p ) = - 33 p ^ { 2 } + 1,254 p - 10,763$