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The revenue $R$, in dollars, derived from selling $x$ computers is given by $R=-3 x^{2}+600 x+1000 .$ (a) How many items should be sold to maximize the revenue? (b) What is the revenue?

(a) $100(\text { b }) 31,000$

Algebra

Chapter 1

Functions and their Applications

Section 4

Quadratic Functions - Parabolas

Functions

Harvey Mudd College

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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02:58

If the total revenue funct…

02:31

A manufacturer's reve…

01:12

The revenue in dollars gen…

01:20

Suppose that the revenue g…

02:52

The profit in dollars in p…

03:45

The revenue $R$ received f…

02:49

01:16

Maximizing Revenue. The re…

08:46

APPLY IT Revenue The margi…

01:34

So they give us the formula. This problem that revenue is equal to negative. Three X squared plus 600 x uh, plus 1000. And without having done the calculus yet, all that we know is that this graph is going to look something like this goes up and then comes back down. So the maximum value is going to be the Vertex. Well, we find the Vertex by doing the formula negative B over two A. So, as you look at this, you can say Okay, well, the B value 600. So it's negative 600 over two times the a value of negative three. So looking at negative 600 divided by 2000 and three is negative. Six. So he gets 600 whatever the units are, uh, sorry. 600 divided by six is 100. Um, I guess items or computers, uh, you know, whatever. Whatever the units are, I circled in green. So then in part B, when it's asking, what is the maximum? Probably knew. Well, now you just have to plug in 100 and for X. Now we go to a calculator. Not that I couldn't do this in my head, but uh huh, I guess I could and replace the excess was 100. So just make sure you do this correctly. You know that one times one times three is negative. Three on 234 zeros six times, one with four zeros, Another one of those. So I was at 30,000. So we're looking at $31,000 and feel free to use a calculator to verify that answer. But this is what we want. That's your answer to A and here's your answer for B chief.

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