Solve the problem. 38) A company\'s monthly sales, in thousands, is given by S(x

Question

Solve the problem. 38) A company's monthly sales, in thousands, is given by S(x, y)-9x0.8y0.4, 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 $2000 on newspaper advertising per month and $5000 on radio advertising per month. What would be the effect on sales if the company increases the amount spent on newspaper advertising to $3000, while the amount spent on radio advertising remains constant?

Explanation / Answer

S= 9x^(0.8)y^(0.4)

Currently x = 2000
and y = 5000

Now, x is made 3000
and y is still 5000

dS/dx ---> partial der of S with x

dS/dx = 9 * 0.8x^(-0.2) * dx * y^(0.4)

We can do this because y remains constant

dS/dx = 7.2 * 2000^(-0.2) * 1000 * 5000^(0.4)

= 47502.28

So, the sales increases by 47502.28 dollars

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