Share Tool + Management Kdan Cloud Topic 4 Questions ΑΞ Tv Tv Ov Comment & Markup T Annotation Editor FAX OCR Q OCR Convert Fax Search Outlines Q Search Optimization Unconstrained optimization Constrained optimization (... (c) Investigate the nature of the critical points using a sign chart for f. 68. A manufacturer produces two types of toys A and B. The production cost for a unit of toy A amounts to €70; the production cost for a unit of toy B is €80. The demand functions for both toys are given by the formulas q₁ = 160 - 2PA + PB and QB = 60+ PA - PB, where PA and PB denote the unit prices for a unit of toy A and B respectively and qд and qɛ denote the amounts demanded. Calculate the selling prices PA and pg that maximize the weekly profit. (It suffices to check that you have found a relative maximum.) ЧА 69. The number of units of a certain product, denoted by q, that can be produced daily depends on the daily available quantities QA and qB of two commodities A and B: q = 10-11 The selling price per unit of the product amounts to €90. Commodities A and B cost €10 and €40 respectively. Find the maximal profit that can be obtained daily. (Again, it suffices to find a relative maximum.) 70. The sum of three non-negative numbers is 1200. What is the maximal value of their product? 71. A box in the form of a cuboid must have a volume of 16 m³. The material for the top and the bottom costs €20 per m². The material for the sides costs €10 per m². What is the minimal cost for the box? 72. Find the dimensions of the rectangular box with a content of 1 m³ and with the smallest total surface (i.e., the surface of all six faces together). 195% Page 21 1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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70,71,72 please

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Management Kdan Cloud
Topic 4 Questions
ΑΞ
Tv Tv Ov
Comment & Markup
T
Annotation
Editor
FAX
OCR
Q
OCR
Convert
Fax
Search
Outlines
Q Search
Optimization
Unconstrained optimization
Constrained optimization (...
(c) Investigate the nature of the critical points using a sign chart for f.
68. A manufacturer produces two types of toys A and B. The production cost for a unit of toy A
amounts to €70; the production cost for a unit of toy B is €80. The demand functions for both toys
are given by the formulas q₁ = 160 - 2PA + PB and QB = 60+ PA - PB, where PA and PB denote
the unit prices for a unit of toy A and B respectively and qд and qɛ denote the amounts demanded.
Calculate the selling prices PA and pg that maximize the weekly profit. (It suffices to check that
you have found a relative maximum.)
ЧА
69. The number of units of a certain product, denoted by q, that can be produced daily depends on the
daily available quantities QA and qB of two commodities A and B: q = 10-11 The selling
price per unit of the product amounts to €90. Commodities A and B cost €10 and €40 respectively.
Find the maximal profit that can be obtained daily. (Again, it suffices to find a relative maximum.)
70. The sum of three non-negative numbers is 1200. What is the maximal value of their product?
71. A box in the form of a cuboid must have a volume of 16 m³. The material for the top and the bottom
costs €20 per m². The material for the sides costs €10 per m². What is the minimal cost for the
box?
72. Find the dimensions of the rectangular box with a content of 1 m³ and with the smallest total surface
(i.e., the surface of all six faces together).
195%
Page 21
1
Transcribed Image Text:Share Tool + Management Kdan Cloud Topic 4 Questions ΑΞ Tv Tv Ov Comment & Markup T Annotation Editor FAX OCR Q OCR Convert Fax Search Outlines Q Search Optimization Unconstrained optimization Constrained optimization (... (c) Investigate the nature of the critical points using a sign chart for f. 68. A manufacturer produces two types of toys A and B. The production cost for a unit of toy A amounts to €70; the production cost for a unit of toy B is €80. The demand functions for both toys are given by the formulas q₁ = 160 - 2PA + PB and QB = 60+ PA - PB, where PA and PB denote the unit prices for a unit of toy A and B respectively and qд and qɛ denote the amounts demanded. Calculate the selling prices PA and pg that maximize the weekly profit. (It suffices to check that you have found a relative maximum.) ЧА 69. The number of units of a certain product, denoted by q, that can be produced daily depends on the daily available quantities QA and qB of two commodities A and B: q = 10-11 The selling price per unit of the product amounts to €90. Commodities A and B cost €10 and €40 respectively. Find the maximal profit that can be obtained daily. (Again, it suffices to find a relative maximum.) 70. The sum of three non-negative numbers is 1200. What is the maximal value of their product? 71. A box in the form of a cuboid must have a volume of 16 m³. The material for the top and the bottom costs €20 per m². The material for the sides costs €10 per m². What is the minimal cost for the box? 72. Find the dimensions of the rectangular box with a content of 1 m³ and with the smallest total surface (i.e., the surface of all six faces together). 195% Page 21 1
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