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Student Government at a University is chartering a plane for Spring Break. The plane can seat 150 passengers. The airline will charge $\$ 120$ per passenger and added to this a surcharge of $\$ 15$ per passenger for each unsold seat. Let $x$ represent the number of unsold seats. (a) Show that the airline's revenue $R=(150-x)(120+15 x) .$ (b) How many seats should be unused to maximize the airline's revenue? (c) What price would each passenger pay if the airline maximized its revenue? (d) Is this a good deal for the Student Government?

$$\text { (b) } 71(\mathrm{c}) \$ 1185$$

Algebra

Chapter 1

Functions and their Applications

Section 4

Quadratic Functions - Parabolas

Functions

Campbell University

University of Michigan - Ann Arbor

Idaho State University

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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No, this problem discusses that student government at a university, They know that they're going on a plane and the plane can see 250 passengers And the charges $120 per passenger, um With a surcharge of a $15 per passenger for each unsold seats. So X. Is the number of unsold seats. And we want to show that the revenue is going to be 150- X. Because we know that if X. is 150, then um that to me times zero, that's how many passengers they can sit, but then we'll get Um Times 1 20 plus 15 X. Because that's the number of passengers that they end up having. So we know that in order to maximize the revenue, they should have 71 unused seats. So we would see that right here based on the curve.

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