Question

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)=

Answer 1