Chapter 14 Homework Solutions Real Analysis

MA30252 Advanced Real Analysis

Course information


Roger Moser
Office: 4W 4.16


Mon9:154E 3.10Problem Class
Tue14:154E 3.38Lecture
Wed10:155W 2.1Lecture

Revision week

There will be a problem class on Tuesday, 9 January, at 2:15pm in 4E 3.38.

Course description/syllabus

Click here for more information about this course from the unit catalogue.


Lecture notes

Here are the lecture notes for this course (with some incomplete references for the moment).

Some of the concepts from the first chapter are discussed in more detail in the notes from one of the predecessors of this course, MA30041 Metric Spaces. These notes may be useful particularly to students who have taken MA20218 Analysis 2A in the academic year 2015/6 or earlier.

Some information about what to expect in the exam can be found here.


Hard copies of the homework assignments will be available in the Wednesday lectures. Alternatively, you can download the problem sheets below. Solutions will be available for download after the hand-in date.


There are numerous books in the library which, collectively, cover the material in the course. Below is a sample list.
  • Kolmogorov, A N and Fomin, S V, Introductory Real Analysis, Dover
  • Kreyszig, E, Introductory Functional Analysis with Applications, Wiley
  • Protter, M H and Morrey, C B, A First Course in Real Analysis, Springer-Verlag
  • Simmons, G F, Introduction to Topology and Modern Analysis, McGraw-Hill
  • Stoll, M, Introduction to Real Analysis, Addison-Wesley
  • Sutherland, W A, Introduction to Metric and Topological Spaces, OUP

14-33(30 min.) Strategic analysis of operating income.1. Kelton is following a product differentiation strategy. Kelton offers a wide selection of clothes and excellent customer service. Kelton’s strategy is to distinguish itself from its competitors and to charge a premium price. 2. Operating income for each year is as follows: 2011 2012 Revenues ($32 u50,000; $31.50 u50,000) $1,600,000 $1,575,000 Costs Costs of goods sold ($15 u50,000; $16.50 u50,000) 750,000 825,000 Selling & customer service costs ($6.50 u62,000); $5.60 u52,000) 403,000 291,200 Purchasing & admin. costs ($80 u780; $65 u620) U62,400UU40,300Total costs U1,215,400UU1,156,500Operating income $ 384,600$ 418,500Change in operating income $33,900 F 3.The Growth Component Revenue effectof growth= Actual units ofoutput soldin 2012±Actual units ofoutput soldin 2011ァゥィィキケククuSellingpricein 2011= (50,000 ±50,000) u$32 = $0 Cost effectof growth forvariable costs= Units of inputrequired toproduce 2012output in 2011ァゥィィィ±Actual units ofinputs usedto produce2011 outputキケククク× Inputpricein 2011Cost effect ofgrowth forfixed costs= Actual units of capacity in2011 because adequate capacity exists to produce2012 output in 2011ァゥィィ±Actualunits ofcapacityin 2011キケクク× Price perunit of capacityin 2011

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