A company finds that the number of new products it develops per year depends on the size of its annual R&D budget, x (in hundreds of thousands of dollars), according to the formula given below. n(x) = −1 + 8x + 2x2 − 0.2x3 (a) Find n''(2) and n''(4). n''(2) = n''(4) = Interpret the results. With $200,000 invested in R&D, the number of new products per $100,000 is increasing at a rate of new products per $100,000 per $100,000, and with $400,000 invested in R&D, it is decreasing at a rate of new products per $100,000 per $100,000. (b) Find the size of the budget that gives the largest rate of return as measured in new products per dollar (again, called the point of diminishing returns). (Round your answer to the nearest cent.) $
A company finds that the number of new products it develops per year depends on the size of its annual R&D budget, x (in hundreds of thousands of dollars), according to the formula given below. n(x) = −1 + 8x + 2x2 − 0.2x3 (a) Find n''(2) and n''(4). n''(2) = n''(4) = Interpret the results. With $200,000 invested in R&D, the number of new products per $100,000 is increasing at a rate of new products per $100,000 per $100,000, and with $400,000 invested in R&D, it is decreasing at a rate of new products per $100,000 per $100,000. (b) Find the size of the budget that gives the largest rate of return as measured in new products per dollar (again, called the point of diminishing returns). (Round your answer to the nearest cent.) $
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
A company finds that the number of new products it develops per year depends on the size of its annual R&D budget, x (in hundreds of thousands of dollars), according to the formula given below.
n(x) = −1 + 8x + 2x2 − 0.2x3
(a)
Find
n''(2) and n''(4).
n''(2)
=
n''(4)
=
Interpret the results.
With $200,000 invested in R&D, the number of new products per $100,000 is increasing at a rate of
new products per $100,000 per $100,000, and with $400,000 invested in R&D, it is decreasing at a rate of
new products per $100,000 per $100,000.
(b)
Find the size of the budget that gives the largest rate of return as measured in new products per dollar (again, called the point of diminishing returns). (Round your answer to the nearest cent.)
$
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