Question

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 = −0.01x + 700      (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'(3,300) =

Interpret your results.

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

Answer 1

Here the speaker's unit is given which also called the demand function and then we calculate the revenue function R(x) and the marginal revenue function is the derivative of revenue function which is given below-