We found that the marketing research department for the company that manufactures and sells memory chips for microcomputers established the following price-demand and revenue functions.

p(x) = 110 - 3x Price demand function
R(x) = xp(x) = x(110 - 3x) Revenue demand function

Where p(x) is the wholesale price in dollars at which x million chips can be sold, and R(x) is in millions of dollars. Both Functions have domain.

a. Find the output that will produce the most revenue.
b. What is the maximum revenue?
c. What is the wholesale price per chip that produces the maximum revenue?

Revenue is the value of all sales of goods and services. It is the total income gotten from the sale of a product. Revenue is the product of the number of items and the price per item.

Given that x = number of items, p(x) = 110 - 3x (price per item)

Revenue (R(x)) = xp(x) = x(110 - 3x)

R(x) = 110x - 3x²

The maximum revenue is at R'(x) = 0. Hence:

R'(x) = 110 - 6x

110 - 6x = 0

6x = 110

x = 18.33

a) The maximum revenue is when 18.33 million chips are produced.

b) R(18.33) = 18.33(110 - 3*18.33) = $1.008 billion

c) p(18.33) = 110 - 3(18.33) =110 - 55 = $55

Cetacea Cetacea · Answer 2 · 2022-02-16T08:33:38+01:00

The following price-demand and revenue functions is :

a) The maximum revenue is when 18.33 million chips are produced.

b) Maximum revenue is $1.008 billion.

c) The wholesale price per chip is $55Revenue is the value of all sales of goods and services.

"Marketing Research Department"

It is the total income gotten from the sale of a product.

Revenue is the product of the number of items and the price per item.

Given :

Part a)

x = number of items

Revenue (R(x)) = xp(x)

Revenue (R(x)) = x(110 - 3x)R(x) =

Revenue (R(x)) = 110x - 3x²

The maximum revenue is at R'(x) = 0.

R'(x) = 110 - 6x110 - 6x = 06x = 110x = 18.33.

The maximum revenue is when 18.33 million chips are produced.

Part b)

The maximum revenue is :

Revenue (R(x)) = xp(x)
R(18.33) = 18.33(110 - 3*18.33)
Revenue (R(x)) = $1.008 billion

Maximum revenue is $1.008 billion.

Part c)

The wholesale price per chip that produces the maximum revenue is :

p(x) = 110 - 3x (price per item)
p(18.33) = 110 - 3(18.33)
p(18.33) =110 - 55
p(18.33)= $55

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