Acme Communication finds that the total revenue function associated with producing a new type of cellular phone is $R ( x ) = 213 x - x ^ { 2 }$
. and the total cost function is C(x)=8000+6 x , where x represents the number of units of cellular phones produced. Find the total profit function, P(x) .
A) $P ( x ) = x ^ { 4 } - 207 x ^ { 2 } + 8000$
B) $P ( x ) = - x ^ { 2 } + 219 x + 8000$
C) $P ( x ) = - 2 x ^ { 2 } + 225 x - 9000$
D) $P ( x ) = - x ^ { 2 } + 207 x - 8000$

Question

Acme Communication finds that the total revenue function associated with producing a new type of cellular phone is $R ( x ) = 213 x - x ^ { 2 }$
. and the total cost function is  C(x)=8000+6 x , where  x  represents the number of units of cellular phones produced. Find the total profit function,  P(x) .
A) $P ( x ) = x ^ { 4 } - 207 x ^ { 2 } + 8000$
B) $P ( x ) = - x ^ { 2 } + 219 x + 8000$
C) $P ( x ) = - 2 x ^ { 2 } + 225 x - 9000$
D) $P ( x ) = - x ^ { 2 } + 207 x - 8000$

Quizplus · Accepted Answer

The total profit function, $P(x)$, is found by subtracting the total cost function, $C(x)$, from the total revenue function, $R(x)$. Therefore, $P(x) = R(x) - C(x) = (213x - x^2) - (8000 + 6x) = -x^2 + 207x - 8000$.

Acme Communication Finds That the Total Revenue Function Associated with Producing