Question

In: Math

1. Average Cost for Producing Microwaves Let the total cost function C(x) be defined as follows....

1. Average Cost for Producing Microwaves

Let the total cost function C(x) be defined as follows.

C(x) = 0.0003x3 − 0.02x2 + 103x + 3,600

Find the average cost function C.

C(x) =

Find the marginal average cost function C '.

C '(x) =

2. Marginal Revenue for Producing Loudspeakers

The management of Acrosonic plans to market the ElectroStat, an electrostatic speaker system. The marketing department has determined that the demand for these speakers is represented by the following function, where p denotes the speaker's unit price (in dollars) and x denotes the quantity demanded. Find the following functions (in dollars), find the value (in dollars) and interpret your results.

p = −0.02x + 890      (0 ≤ x ≤ 20,000)

(a)

Find the revenue function R.

R(x) =

(b)

Find the marginal revenue function R'(x).

R'(x) =

(c)

Compute the following value.

R'(8,200) =

Interpret your results.

When the level of production is  units, the production of the next speaker system will bring an additional revenue of  dollars.

3.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 + 190

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) = 0.000001x3 − 0.02x2 + 140x + 75,000

(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'(1,500)=R'(1,500)=P'(1,500)=

Solutions

Expert Solution


Related Solutions

For the following exercises, the cost of producing x cellphones is described by the function C(x) = x2 − 4x + 1000. Find the average rate of change in the total cost as x changes from x = 10 to x = 15.
For the following exercises, the cost of producing x cellphones is described by the function C(x) = x2 − 4x + 1000. Find the average rate of change in the total cost as x changes from x = 10 to x = 15.
Let f be the periodic function defined by f(x) = 1 + x|x|, −1 < x...
Let f be the periodic function defined by f(x) = 1 + x|x|, −1 < x < 1, and f(x) = f(x + 2). Find the Fourier series of f.
Solve the problem. Let C(x) be the cost function and R(x) the revenue function. Compute the...
Solve the problem. Let C(x) be the cost function and R(x) the revenue function. Compute the marginal cost, marginal revenue, and the marginal profit functions. C(x) = 0.0004x3 - 0.036x2 + 200x + 30,000 R(x) = 350x Select one: A. C'(x) = 0.0012x2 - 0.072x + 200 R'(x) = 350 P'(x) = 0.0012x2 - 0.072x - 150 B. C'(x) = 0.0012x2 + 0.072x + 200 R'(x) = 350 P'(x) = 0.0012x2 + 0.072x + 150 C. C'(x) = 0.0012x2 -...
1) The marginal cost function associated with producing x widgets is given by C'(x)= -0.8x+75 where...
1) The marginal cost function associated with producing x widgets is given by C'(x)= -0.8x+75 where C'(x) is measured in dollars/unit and x denotes the number of widgets. Find the total cost C(x) incurred from producing the 11th through 05th units of the day. The options are: 2040 2030 2020 2000 2050 a) The Math Club has determined that in order to successfully tutor x Math 2 students in preparation for the second homework, the price per student p(x) in...
Let g be the function defined by g(x) = x(x + 1). Find g(x + h)...
Let g be the function defined by g(x) = x(x + 1). Find g(x + h) − g(x − h).
Find the cost function if the marginal cost function is given by C' (x) = x^1/3...
Find the cost function if the marginal cost function is given by C' (x) = x^1/3 +9 and 27 units cost ​$415. C(x) =
6. (a) let f : R → R be a function defined by f(x) = x...
6. (a) let f : R → R be a function defined by f(x) = x + 4 if x ≤ 1 ax + b if 1 < x ≤ 3 3x x 8 if x > 3 Find the values of a and b that makes f(x) continuous on R. [10 marks] (b) Find the derivative of f(x) = tann 1 1 ∞x 1 + x . [15 marks] (c) Find f 0 (x) using logarithmic differentiation, where f(x)...
Let the total cost function be C (q) = 50 + 2q + 0:5q2. For what...
Let the total cost function be C (q) = 50 + 2q + 0:5q2. For what values of q we have economies of scale?
Let the joint pmf of X and Y be defined by f (x, y) = c(x...
Let the joint pmf of X and Y be defined by f (x, y) = c(x + y), x =0, 1, 2, y = 0, 1, with y ≤ x. 1. Are X and Y independent or dependent? Why or why not? 2. Find g(x | y) and draw a figure depicting the conditional pmfs for y =0 and 1. 3. Find h(y | x) and draw a figure depicting the conditional pmfs for x = 0, 1 and2. 4....
Let the joint pmf of X and Y be defined by f (x, y) = c(x...
Let the joint pmf of X and Y be defined by f (x, y) = c(x + y), x =0, 1, 2, y = 0, 1, with y ≤ x. 1. Find g(x | y) and draw a figure depicting the conditional pmfs for y =0 and 1. 2. Find h(y | x) and draw a figure depicting the conditional pmfs for x = 0, 1 and2. 3. Find P(0 < X <2 |Y = 0), P(X ≤ 2 |Y...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT