Revenue generated by producing products.

Question

Suppose the revenue R in thousands of dollars that a company receives from producing x thousand compact disc players is given by the formula :R(x)= x(30-3x)
a. Evaluate ?R(4?) and interpret the result.
b. How many CD players should the company produce to maximize its? revenue?
c. What is the maximum? revenue?

Answer 1

R(4) = 4(30 - 3 * 4) = 4(30 - 12) = 4(18) = $72K (K is used to represent $1000)

 

When 4000 CD players are produced, the company earns $72,000 in revenue

 

To determine where the company will maximize revenue, find the derivative of R(x) and set it equal to zero.

 

R(x)= x(30 - 3x) = 30x - 3x²

 

R'(x) = 30 - 6x = 0

 

30 = 6x 

 

x = 5, so when the company produces 5000 CD players, it will maximize its revenue

 

The amount of revenue will be R(5) = 5(30 - 3 * 5) = 5(30 - 15) = 5(15) = $75K or $75,000

Answer 2

R(x)= x(30-3x)

R(4)= 4(30-3(4)) by plugging 4 in for all x

R(4) = 4(30-12)

       = 4(18)

       = 72

 

so when a company produces 4,000 CD players, their revenue is $72,000