How to solve this question

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

Evaluate s(x,y) at the two specified (x,y) points and take the difference.

 

x₁ = 5

y₁ = 3

 

x₂ = 6

y₂ = 3

 

s(x,y) = 9x^0.8y^0.5

 

s(x₁,y₁) = 9(5^0.8)(3^0.5) ≅ 56.491

s(x₂,y₂) = 9(6^0.8)(3^0.5) ≅ 65.362

 

s(x₂,y₂) - s(x₁,y₁) = 65.362 - 56.491 = 8.871

 

The monthly sales in thousands increases by 8.871, that is, by $8,871.