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777dan777 [17]
3 years ago
10

The management of Acrosonic plans to market the ElectroStat, an electrostatic speaker system. The marketing department has deter

mined 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 + 610 (0 ≤ x ≤ 20,000)

a. Find the revenue function R.
b. Find the marginal revenue function R'(x).
c. Compute the following value.
R'(5,400) = _______________
Mathematics
1 answer:
crimeas [40]3 years ago
5 0

Answer:

(a)R(x)=-0.02x^2+610x

(b)R'(x)=-0.04x+610

(c)R'(5400)=$394

Step-by-step explanation:

Given that x is the quantity demanded and the speaker's unit price (in dollars) is p where:

p = −0.02x + 610 (0 ≤ x ≤ 20,000)

(a)Revenue function R.

Revenue = Price X Quantity Demanded

Therefore:

R(x)=xp

=x(-0.02x + 610)\\R(x)=-0.02x^2+610x

(b)Marginal revenue function R'(x)

If R(x)=-0.02x^2+610x

Then, the marginal revenue function

R'(x)=-0.04x+610

(c)We want to compute R'(5,400)

R'(5400)=-0.04(5400)+610\\R'(5400)=394

From the above, we can infer that the revenue that will be generated on the sales of the 5401st item is $394.

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