A company manufactures a series of 20-in. flat-tube LCD televisions. The quantity x of these sets demanded each week is related to the wholesale unit price p by the following equation. p = −0.007x + 200 The weekly total cost (in dollars) incurred by Pulsar for producing x sets is represented by the following equation. Find the following functions (in dollars) and compute the following values. C(x) = 0.000003x3 − 0.01x2 + 150x + 70,000 (a) Find the revenue function R. R(x) = Find the profit function P. P(x) =
A company manufactures a series of 20-in. flat-tube LCD televisions. The quantity x of these sets demanded each week is related to the wholesale unit price p by the following equation. p = −0.007x + 200 The weekly total cost (in dollars) incurred by Pulsar for producing x sets is represented by the following equation. Find the following functions (in dollars) and compute the following values. C(x) = 0.000003x3 − 0.01x2 + 150x + 70,000 (a) Find the revenue function R. R(x) = Find the profit function P. P(x) =
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.3: Algebraic Expressions
Problem 3E
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Marginal Cost, Revenus, and Profit for Producing LCD TVs
A company manufactures a series of 20-in. flat-tube LCD televisions. The quantity x of these sets demanded each week is related to the wholesale unit price p by the following equation.p = −0.007x + 200
The weekly total cost (in dollars) incurred by Pulsar for producing x sets is represented by the following equation. Find the following functions (in dollars) and compute the following values.
C(x) = 0.000003x3 − 0.01x2 + 150x + 70,000
(a)
Find the revenue function R.
R(x) =
Find the profit function P.
P(x) =
(b)
Find the marginal cost function C'.
C'(x) =
Find the marginal revenue function R'.
R'(x) =
Find the marginal profit function P'.
P'(x) =
(c)
Compute the following values. (Round your answers to two decimal places.)
C'(2,500) =R'(2,500) =P'(2,500) =
and graphs
Transcribed Image Text:(d) Sketch C(x).
C (in millions)
C (in millions)
C (in millions)
1.2
1.2
1.2
0.8
0.8
0.8
0.4
0.4
0.4
x (in thousands)
10
x (in thousands)
10
x (in thousands)
10
8
4
6
8
2 4
8
-0.4
-0.4
-0.4
C (in millions)
1.2
0.8
0.4
x (in thousands)
10
4 6
8
-0.4
Sketch R(x).
R (in millions)
R (in millions)
R (in millions)
2.4
2.0
2.4
2.0
2.4
2.0
1.6
1.6
1.6
1.2
1.2
1.2
0.8
0.8
0.8
0.4
0.4
0.4
x (in thousands)
x (in thousands)
x (in thousands)
5 10 15 20 25 30 35 40 45
5 10 15 20 25 30 35 40 45
5 10 15 20 25 30 35 40 45
R (in millions)
2.4
2.0
1.6
1.2
0.8
0.4
x (in thousands)
5 10 15 20 25 30 35 40 45
Transcribed Image Text:Sketch P(x).
P (in millions)
500아
400
P (in millions)
50아
400
P (in millions)
500아
400
300
200
300
300
200
200
100
100
100
- x (in thousands)
10 12
- x (in thousands)
10 12
- x (in thousands)
10 12
2 4 6
8
2 4 6 8
2 4 6 8
P (in millions)
500아
400
300
200
100
x (in thousands)
2 4 6 8
10 12
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