1. Average Cost for Producing Microwaves

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

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 ProducingLoudspeakers

The management of Acrosonic plans to market the ElectroStat, anelectrostatic speaker system. The marketing department hasdetermined that the demand for these speakers is represented by thefollowing function, where p denotes the speaker's unitprice (in dollars) and x denotes the quantity demanded.Find the following functions (in dollars), find the value (indollars) 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 productionof the next speaker system will bring an additional revenueof  dollars.

3.Marginal Cost, Revenus, and Profit for Producing LCDTVs

A company manufactures a series of 20-in. flat-tube LCDtelevisions. The quantity x of these sets demanded eachweek is related to the wholesale unit price p by thefollowing equation.

p = ?0.007x + 190

The weekly total cost (in dollars) incurred by Pulsar forproducing x sets is represented by the following equation.Find the following functions (in dollars) and compute the followingvalues.

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 decimalplaces.)

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