Marketing—Advertising Budget: The PowerSet Company has estimated that the monthly amount spent on advertising and the sales of its Side-Out Volleyballs can be modeled by
f(x) = 189.24x − 3.5x2 0 ≤ x ≤ 25
where x represents the amount spent on advertising in thousands of dollars and f(x) represents the number of volleyballs sold, in hundreds.
(a) Determine the differential dy for the model.
(b) The company’s director of advertising has increased the advertising budget from $10,000 to $11,000. Use the differential to approximate the increase in sales by increasing the amount spent on advertising from x = 10 to x = 11.
(c) Compute the actual change in sales Δy = f(11) − f(10) and compare Δy to the approximation dy found in part (b).
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