Solve the problem.
-A charter flight charges a fare of $\$ 400$ per person plus $\$ 4$ per person for each unsold seat on the plane. If the plane holds 176 passengers and if $x$ represents the number of unsold seats, an expression for the total revenue received for the flight is $R(x)=(176-x)(400+4 x)$. Find the maximum revenue.
A) $\$ 152,352$
B) $\$ 76,676$
C) $\$ 76,176$
D) $\$ 71,676$

Question

Quizplus · Accepted Answer

The expression for revenue is a quadratic function, which is maximized at its vertex. The vertex of $R(x) = (176-x)(400+4x)$ occurs at $x = \frac{-b}{2a}$. Expanding and simplifying gives $R(x) = -4x^2 + 304x + 70400$. The vertex is at $x = \frac{-304}{-8} = 38$. Substituting $x = 38$ into the revenue function gives the maximum revenue of $\$ 76,176$.

Solve the Problem $400\$ 400$400 Per Person Plus $4\$ 4$4 Per Person for Each Unsold Seat on the Plane

Solve the Problem $\$ 400$ Per Person Plus $\$ 4$ Per Person for Each Unsold Seat on the Plane