A company\'s monthly sales, in thousands, is given by S(x, y) = 7x^0.4 y^0.5, wh

Question

A company's monthly sales, in thousands, is given by S(x, y) = 7x^0.4 y^0.5, 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 company currently spends $4000 on newspaper advertising per month and $3000 on radio advertising per month. What would be the effect on sales if the company increases the amount spent on newspaper advertising to $5000, while the amount spent on radio advertising remains constant?

Explanation / Answer

It is very evident that the function S is giving the sales as a function of amount spent on newspaper (x) and radio (y) advertisements

first calculating S at x= $4000 and y = $3000

S=7*$4000^(0.4)*$3000^(0.5) = 10579.93 ( in thousands)

and calculating S at x=$5000 and y=$3000

S=7*5000^(0.4)*3000^(0.5) = 11567.69 ( in thousands)

it is obvious that the sales increase when the spending on advertisement increase and the sales have increased by 987.76 ( in thousands) which is 9.34%

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