a company's monthly sales, in thousands, is given by s(x,y)=9x^.8y^.5. where x is the amount spent on newspaper advertising per month in thousands of dollars and y is the amount spent on radio advertising per month in thousands of dollars. Suppose the comany currently spends $5000 on newspaper advertising per month and $3000 pm radop advertising per month. What would be the effect on sales if the company increases the amount spent on newspaper advertising to $6000, while the amount spent on radio advertising remains constant?

Question

a company's monthly sales, in thousands, is given by s(x,y)=9x^.8y^.5. where x is the amount spent on newspaper advertising per month in thousands of dollars and y is the amount spent on radio advertising per month in thousands of dollars. Suppose the comany currently spends $5000 on newspaper advertising per month and $3000 pm radop advertising per month. What would be the effect on sales if the company increases the amount spent on newspaper advertising to $6000, while the amount spent on radio advertising remains constant?

Answer 1

it would grow by a factor of (6/5)^.8

Answer 2

To determine the effect on sales given the changes in advertising spending, we need to calculate the new sales value using the provided function.

Given:
s(x, y) = 9x^0.8 * y^0.5
Where:
x = amount spent on newspaper advertising per month in thousands of dollars
y = amount spent on radio advertising per month in thousands of dollars

Current spending:
x = $5000 (newspaper advertising)
y = $3000 (radio advertising)

To find the current sales value, substitute the values of x and y into the sales function:

s(5000, 3000) = 9 * 5000^0.8 * 3000^0.5

Now, let's calculate the current sales value:

s(5000, 3000) ≈ 9 * (56.234) * (54.772) ≈ 27,860.150

Hence, the current monthly sales are approximately $27,860.150.

Now, let's consider the effect of increasing the amount spent on newspaper advertising to $6000 while keeping radio advertising constant at $3000.

Updated spending:
x = $6000 (newspaper advertising)
y = $3000 (radio advertising)

We need to calculate the new sales value using the updated spending. Substitute the new values of x and y into the sales function:

s(6000, 3000) = 9 * 6000^0.8 * 3000^0.5

Now, let's calculate the new sales value:

s(6000, 3000) ≈ 9 * (67.082) * (54.772) ≈ 32,403.473

Hence, the new monthly sales would be approximately $32,403.473.

Comparing the current and new sales values, we can see that increasing the amount spent on newspaper advertising from $5000 to $6000, while keeping radio advertising constant at $3000, leads to an increase in monthly sales from approximately $27,860.150 to $32,403.473.