Question

Marginal Cost, Revenue, 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 = 750 - 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) = 0.000004x^3 - 0.03x^2 + 350x + 75,000 (a) Find the revenue function R. R(x) = 750x - 0.06x^2 Find the profit function P. P(x) = -0.000004x^3 - 0.03x^2 + 400x - 75000 (b) Find the marginal cost function C'. C'(x) = 0.000004x^3 - 0.03x^2 + 350x + 75000 Find the marginal revenue function R'. R'(x) = -0.12x + 750 Find the marginal profit function P'. P'(x) = -0.000012x^2 - 0.06x + 1100 (c) Compute the following values. (Round your answers to two decimal places.) C'(2,000) = R'(2,000) = 510 P'(2,000) =

          Marginal Cost, Revenue, 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 = 750 - 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) = 0.000004x^3 - 0.03x^2 + 350x + 75,000

(a) Find the revenue function R.
R(x) = 750x - 0.06x^2

Find the profit function P.
P(x) = -0.000004x^3 - 0.03x^2 + 400x - 75000

(b) Find the marginal cost function C'.
C'(x) = 0.000004x^3 - 0.03x^2 + 350x + 75000

Find the marginal revenue function R'.
R'(x) = -0.12x + 750

Find the marginal profit function P'.
P'(x) = -0.000012x^2 - 0.06x + 1100

(c) Compute the following values. (Round your answers to two decimal places.)
C'(2,000) =
R'(2,000) = 510
P'(2,000) =

Show more…

Marginal Cost, Revenue, 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 = 750 - 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) = 0.000004x^3 - 0.03x^2 + 350x + 75,000

(a) Find the revenue function R.
R(x) = 750x - 0.06x^2

Find the profit function P.
P(x) = -0.000004x^3 - 0.03x^2 + 400x - 75000

(b) Find the marginal cost function C'.
C'(x) = 0.000004x^3 - 0.03x^2 + 350x + 75000

Find the marginal revenue function R'.
R'(x) = -0.12x + 750

Find the marginal profit function P'.
P'(x) = -0.000012x^2 - 0.06x + 1100

(c) Compute the following values. (Round your answers to two decimal places.)
C'(2,000) =
R'(2,000) = 510
P'(2,000) =

Added by Ruth C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

02/02/2023

Step 1

This can be found by multiplying the weekly cost of the LED television by the quantity demanded. C(x) = 750 * 06x * x Show more…

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Title: Marginal Cost, Revenue, and Profit for Producing LED TVs The weekly demand for the Pulsar 25 color LED Television is represented by Q, which denotes the quantity demanded. The wholesale unit price is denoted by P in dollars. 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 sets. The function is as follows: C(x) = 0.000004x^3 + 0.03x^2 + 350x + 75,000 (x < 12,000) Find the revenue function R: R(x) = Px = 75x - 0.06x^2 Find the profit function: P(x) = R(x) - C(x) = (75x - 0.06x^2) - (0.000004x^3 + 0.03x^2 + 350x + 75,000) Find the marginal cost function C': C'(x) = 0.000012x^2 + 0.06x + 350 Find the marginal revenue function R': R'(x) = 75 - 0.12x Find the marginal profit function P': P'(x) = -0.000012x^2 + 0.12x - 1100 Compute the following values: C'(2,000) R'(2,000) P'(2,000)

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00:01 Hi, in this question given that the profit p equals 750 minus 0 .06 x, where x varies from 0 less than are equal to x less than are equal to 12 ,000.

00:15 And also given that the cost function c of x equals 0 .00000 4 x cube minus 0 .03 x squared plus 350 .000 .000 .5x squared plus 350.

00:30 X plus 75 ,000.

00:35 In part a, first we need to find the revenue function, that is or of x, which is equal to p into x, which is equal to 750 minus 0 .06 x into x.

00:49 On multiplying we get 750x minus 0 .06 x squared.

00:59 Therefore, or of x equals 750x minus 0 .06 x squared.

01:07 Next, we need to find the p of x, that is found by using the formula r of x minus c of x, which is equal to 750x minus 0 .06 x squared minus 0 .004 x cube plus 0 .03x squared.

01:35 Minus 350 x minus 75 ,000.

01:43 On further simplification, we get minus 0 .00004 x cube minus 0 .0 .03x squared plus 400x minus 75 ,000.

01:57 Which is the final answer for the function p of x.

01:57 Next, point 0 .03x squared plus 400 x minus 75, which is the final answer for the function p of x.

02:06 Next, for part b, we need to find c dash of x.

02:15 On differentiating c of x with respect to x, then we get minus 0 .0000001 to x2x2x2x2x2x2.

02:26 X squared minus 0 .0 .066x plus 3.

02:30 Next, we need to find the or dash of x...

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