The weekly revenue ($) from the sale two type of speakers is 3 1 R(x, y) = -1x² - y² - xy xy +300x + 240y 4 where x is the shelf ready speaker and y is the speaker kit. The weekly cost to produce chese items is C(x, y) = 180x + 140y + 5000 dollars. Determine how many of each item should be produced weekly to maximize the company's profit by answering the following. (a) Write the profit function, P(x, y) = R(x, y) — C(x, y). (b) Find the critical points of P. (c) Find the second order partial derivatives of P. (d) Find D(a, b) and prove this point is a relative maximum. (e) State the number of each speaker to be produced and the profit to be gained from producing them.
The weekly revenue ($) from the sale two type of speakers is 3 1 R(x, y) = -1x² - y² - xy xy +300x + 240y 4 where x is the shelf ready speaker and y is the speaker kit. The weekly cost to produce chese items is C(x, y) = 180x + 140y + 5000 dollars. Determine how many of each item should be produced weekly to maximize the company's profit by answering the following. (a) Write the profit function, P(x, y) = R(x, y) — C(x, y). (b) Find the critical points of P. (c) Find the second order partial derivatives of P. (d) Find D(a, b) and prove this point is a relative maximum. (e) State the number of each speaker to be produced and the profit to be gained from producing them.
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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Transcribed Image Text:The weekly revenue ($) from the sale two type of speakers is
3
8
R(x, y)
==
1
+²
4
1
4xy +300x + 240y
where x is the shelf ready speaker and y is the speaker kit. The weekly cost to produce
these items is
(b) Find the critical points of P.
C(x, y) = 180x + 140y + 5000
dollars. Determine how many of each item should be produced weekly to maximize the
company's profit by answering the following.
(a) Write the profit function, P(x, y) = R(x, y) — C(x, y).
(c) Find the second order partial derivatives of P.
(d) Find D(a, b) and prove this point is a relative maximum.
(e) State the number of each speaker to be produced and the profit to be gained from
producing them.
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