A company is selling tables at a price of $400 each. The total cost required to produce x tables is $C ( x ) = 2 x ^ { 2 } + 80 x + 6000$ The maximum profit of this company, in dollars, is

A)6,800
B)7,000
C)7,200
D)7,500
E)8,000

Question

A company is selling tables at a price of $400 each. The total cost required to produce x tables is $C ( x ) = 2 x ^ { 2 } + 80 x + 6000$ The maximum profit of this company, in dollars, is

A)6,800
B)7,000
C)7,200
D)7,500
E)8,000

Quizplus · Accepted Answer

The maximum profit occurs at the vertex of the parabola representing the profit function, which is $P(x) = R(x) - C(x) = 400x - (2x^2 + 80x + 6000)$. The vertex of a parabola in the form $y = ax^2 + bx + c$ is at $x = -b/2a$. In this case, $a = -2$ and $b = -80$, so the vertex is at $x = -(-80)/2(-2) = 20$. The profit at this point is $P(20) = 400(20) - (2(20)^2 + 80(20) + 6000) = 8000 - (800 + 1600 + 6000) = 6800$.

A Company Is Selling Tables at a Price of $400 C(x)=2x2+80x+6000C ( x ) = 2 x ^ { 2 } + 80 x + 6000C(x)=2x2+80x+6000

A Company Is Selling Tables at a Price of $400 $C ( x ) = 2 x ^ { 2 } + 80 x + 6000$