both images are one question Marginal Cost, Revenus, and Profit for Producing LED TVs The weekly demand for the Pulsar 25 color LED television is represented by p, where p denotes the wholesale unit price in dollars and x denotes thequantity demanded.p = 700- 0.06x(0 < x < 12,000)The weekly total cost function associated with manufacturing the Pulsar 25 is given by C(x), where C(x) denotes the total cost (in dollars) incurred in producing x sets. Find the following functions (in dollars) and compute thefollowing values.C(x) = 0.000005x³ – 0.03x2 + 530x + 75,000%3D(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) :%3D(c) Compute the following values. (Round your answers to two decimal places.)C'(1,000)R'(1,000)P'(1,000) (d) Sketch C(x).CCC2000 4000 6000 8000 10 00012 000X2000 4000 6000 8000 10 00012 0001x 10-1x 106-5.0 x 10°8×10°2000 4000 6000 8000 10 00012 000-2x10-1.0 x 107-2x106×104x 106-3x 10-1.5 x 107-4x102x 106® O-2.0×107-6x10°2000 4000 6000 8000 10000 12 000Sketch R(x).8x10°2.0 × 10°R6×1061.5 x 10'1.5 x 102000 4000 6000 8000 1000012 0004× 1061.0 × 10-2x1061.0 × 102x106-4x10500 0005.0× 10-6x102000 4000 6000 8000 10000 12 0002000 4000 6000 8000 10 00012 002000 4000 6000 8000 1000012 000-8x106Sketch P(x).PP2.0 × 1062000 4000 0000 8000 1000012 0002000400060008000 10 000 12000- 2x106-4x 10-0.011x1071.5x 10-0.028×10-6x 10°-0.031.0 x 106x106-8x 106-0.044×106500 000-1x 10'-0.052x 10о-0.062000 4000 6000 8000 1000012 0002000 4000 6000 8000 10000 12 000

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Description: both images are one question Marginal Cost, Revenus, and Profit for Producing LED TVs The weekly demand for the Pulsar 25 color LED television is represented by p, where p denotes the wholesale unit price in dollars and x denotes thequantity demanded

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Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.6: Inequalities

Problem 88E

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Marginal Cost, Revenus, and Profit for Producing LED TVs The weekly demand for the Pulsar 25 color LED television is represented by p, where p denotes the wholesale unit price in dollars and x denotes the
quantity demanded.
p = 700
- 0.06x
(0 < x < 12,000)
The weekly total cost function associated with manufacturing the Pulsar 25 is given by C(x), where C(x) denotes the total cost (in dollars) incurred in producing x sets. Find the following functions (in dollars) and compute the
following values.
C(x) = 0.000005x³ – 0.03x2 + 530x + 75,000
%3D
(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) :
%3D
(c) Compute the following values. (Round your answers to two decimal places.)
C'(1,000)
R'(1,000)
P'(1,000)

(d) Sketch C(x).
C
C
C
2000 4000 6000 8000 10 00012 000
X
2000 4000 6000 8000 10 00012 000
1x 10
-1x 106
-5.0 x 10°
8×10°
2000 4000 6000 8000 10 00012 000
-2x10
-1.0 x 107
-2x10
6×10
4x 106
-3x 10
-1.5 x 107
-4x10
2x 106
® O-2.0×107
-6x10°
2000 4000 6000 8000 10000 12 000
Sketch R(x).
8x10°
2.0 × 10°
R
6×106
1.5 x 10'
1.5 x 10
2000 4000 6000 8000 1000012 000
4× 106
1.0 × 10
-2x106
1.0 × 10
2x106
-4x10
500 000
5.0× 10
-6x10
2000 4000 6000 8000 10000 12 000
2000 4000 6000 8000 10 00012 00
2000 4000 6000 8000 1000012 000
-8x106
Sketch P(x).
P
P
2.0 × 106
2000 4000 0000 8000 1000012 000
2000
4000
6000
8000 10 000 12000
- 2x106
-4x 10
-0.01
1x107
1.5x 10
-0.02
8×10
-6x 10°
-0.03
1.0 x 10
6x106
-8x 106
-0.04
4×106
500 000
-1x 10'
-0.05
2x 10
о-0.06
2000 4000 6000 8000 1000012 000
2000 4000 6000 8000 10000 12 000

Expert Solution

Step 1

(a)

The revenue function is product of quantity demanded times the demand function.

So, $R (x) = x \cdot p = x (700 - 0.06 x) = 700 x - 0.06 x^{2}$ .

The profit function is just the difference of revenue function and cost function.

So, $P (x) = R (x) - C (x) = 700 x - 0.06 x^{2} - (0.000005 x^{3} - 0.03 x^{2} + 530 x + 75000) = - 0.000005 x^{3} - 0.09 x^{2} + 170 x - 75000$

(b)

Marginal cost is the first derivative of cost function.

So, $C' (x) = 0.000015 x^{2} - 0.06 x + 530$ .

The marginal revenue is the first derivative of the revenue function.

So, $R' (x) = 700 - 0.12 x$ .

The marginal profit is the first derivative of profit function.

So, we get $P' (x) = - 0.000015 x^{2} - 0.18 x + 170$ .

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