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The management of Acrosonic plans to market the ElectroStat, an electrostatic sp

ID: 2845074 • Letter: T

Question

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.

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. p = -0.02x + 820 (0 x 20,000) Find the revenue function R. R(x) = Find the marginal revenue function R'(x). R'(x) = Compute the following value. R'(7700) = Interpret your results. When the level of production is units, the production of the next speaker system will bring an additional revenue of dollars. Acrosonic's production department estimates that the total cost (in dollars) incurred in manufacturing x ElectroStat speaker systems in the first year of production will be represented by the following function, where R(x) is the revenue function in dollars and x denotes the quantity demanded. C(x) = 140x + 26000 and R(x) = -0.04x2 + 800x Find the profit function P. P(x) = Find the marginal profit function P '. P '(x) = Compute the following values. P '(3000) = P '(9400) =

Explanation / Answer

The revenue function is

R (x) = px = ( -0:02x + 820) x = -0.02x^2+ 820x.

(b) The marginal revenue function is

R(x) = -0:04x + 820.

(c) R(7700) = -0.04*(7700) + 820 = 512. So, if the 7701st speaker is been produced

and sold, the revenue increases approximately 512 dollars.


2.P(x)= -.04x^2+660x-26000

P'(x)= -.08x+660

P(3000) = (-.08*3000)-26000= -26240

P(9400)= (-.08*9400)-26000=26752