The marketing department at Texas Instruments has found that when certain calculators are sold at a price of p dollars per unit, the number x of calculators sold is given by the demand equation x = 21,000 – 150p (a) Find a model that expresses the revenue R as a function of the price p. (b) What is the domain of R? (c) What unit price should be used to maximize revenue? (d) If this price is charged, what is the maximum revenue? (e) How many units are sold at this price?
The marketing department at Texas Instruments has found that when certain calculators are sold at a price of p dollars per unit, the number x of calculators sold is given by the demand equation x = 21,000 – 150p (a) Find a model that expresses the revenue R as a function of the price p. (b) What is the domain of R? (c) What unit price should be used to maximize revenue? (d) If this price is charged, what is the maximum revenue? (e) How many units are sold at this price?
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Transcribed Image Text:1 Build Quadratic Models from Verbal Descriptions
In economics, revenue R, in dollars, is defined as the amount of money received
from the sale of an item and is equal to the unit selling price p, in dollars, of the item
times the number x of units actually sold. That is,
R= xp
In economics, the Law of Demand states that p and x are related: As one
increases, the other decreases. The equation that relates p and x is called the demand
equation. When the demand equation is linear, the revenue model is a quadratic
function.
1
Maximizing Revenue
The marketing department at Texas Instruments has found that when certain
calculators are sold at a price of p dollars per unit, the number x of calculators sold
is given by the demand equation
x = 21,000 – 150p
(a) Find a model that expresses the revenue R as a function of the price p.
(b) What is the domain of R?
(c) What unit price should be used to maximize revenue?
(d) If this price is charged, what is the maximum revenue?
(e) How many units are sold at this price?
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