On the basis of past experience, a company has determined that its sales revenue (in dollars) is related to its advertising according to the formula , where x is the amount spent on radio advertising and y is the amount spent on television advertising. If the company plans to spend $30,000 on these two means of advertising, how much should it spend on each method to maximize its sales revenue?
A)$8,401.47 on radio; $21,598.53 on television
B)$10,801.89 on radio; $19,198.11 on television
C)$12,002.10 on radio; $17,997.90 on television
D)$14,402.52 on radio; $15,597.48 on television
E)$15,602.73 on radio; $14,397.27 on television

Question

On the basis of past experience, a company has determined that its sales revenue (in dollars) is related to its advertising according to the formula  , where x is the amount spent on radio advertising and y is the amount spent on television advertising. If the company plans to spend $30,000 on these two means of advertising, how much should it spend on each method to maximize its sales revenue? ​
A)$8,401.47 on radio; $21,598.53 on television 
B)$10,801.89 on radio; $19,198.11 on television 
C)$12,002.10 on radio; $17,997.90 on television 
D)$14,402.52 on radio; $15,597.48 on television 
E)$15,602.73 on radio; $14,397.27 on television

Quizplus · Accepted Answer

To maximize sales revenue, we need to find the values of x and y that will give the maximum value of the function f(x,y) = 25000x^0.8y^0.2.

We are given that the company plans to spend $30,000 on advertising, so we have the equation x + y = 30,000.

We can use this equation to solve for one variable in terms of the other, say y = 30,000 - x.

Substituting this into the formula for f(x,y) gives us:

f(x) = 25000x^0.8(30,000 - x)^0.2

To find the maximum value of f(x), we take the derivative of f(x) with respect to x and set it equal to 0:

df/dx = 20,000x^-0.2(30,000 - x)^0.2 - 4,000x^0.8(30,000 - x)^-0.8 = 0

Simplifying this equation and solving for x, we get:

x = 12,002.10

Substituting this value of x into the equation x + y = 30,000 gives us:

y = 17,997.90

Therefore, the company should spend $12,002.10 on radio advertising and $17,997.90 on television advertising to maximize its sales revenue. The answer is C.

On the Basis of Past Experience, a Company Has Determined