MATH1003 Assessment 3 S1 2022 1

MATH1003 Assessment 3 S1 2022 1
MATH1003 QUANTITATIVE METHODS WITH ECONOMICS
ASSESSMENT 3: CALCULATIONS
Due 11pm Sunday Week 13
Value 45%
Modules 3, 4 and 5
Please follow these guidelines for the assignment
 You must attempt and submit responses for all three questions
 The assessment must be submitted online as a SINGLE Word file with Excel output copied
and pasted (use Paste special –> Enhanced Metafile/Excel Object).
 All submissions should be typed including the mathematics in A4 page size
 All written descriptions must be in correctly structured sentences using appropriate
mathematical, business and English language.
 Descriptions should be in formal language (e.g. third person ‐no use of I or me throughout).
 Figures and tables must be fully labelled and include headings.
All the information you need is given in the question or in your study material.
However if you happen to use other resources ensure that they are referenced using standard practice
taught in EDUC1001 and/or ENGL1002.
All submitted work must be your own. Working too closely with other students and submitting close to
identical work can be deemed as collusion. Using others’ work as if it is your own can be deemed to be
plagiarism.
Your assessment must be submitted online in a single Word file.
MATH1003 Assessment 3 S1 2022 2
W’ght
in % Criterion Excellent (HD) Very Good (D) Good (C) Satisfactory (P) Unsatisfactory (F) Not Present 50 (Q1), 40 (Q2 + 3)
Calculations
 Relevant to the question
 Accurate
 Correctly set out
 Appropriate rounding
Includes units with
measurements.
The calculations are
highly related to the
task; Excellent
calculations high
level of mathematical
setting out, rounding
and measurements.
The calculations are
closely related to the
task; Advanced
calculations,
advanced setting out,
rounding and
measurements.
The calculations are
related to the task;
Competent
calculations,
competent setting
out, rounding and
measurements.
The calculations are
partially related to
the task; Adequate
calculations with
some errors, basic
setting out,
rounding and
measurements.
The calculations
are not related to
the task;
Calculations are
incorrect. Poor
mathematical
setting out,
Calculations
absent;
25 (Q2 + 3)
Use of Excel (Questions 2 and 3)
 correct tables and/or graphs
 graphs relevant to the
question
 graphs fully labelled
Highly advanced use
of Excel to draw
graphs, graphs are
fully labelled and
relevant to the
question.
Advanced use of
Excel to draw graphs,
graphs are fully
labelled with minor
errors and relevant
to the question.
Effective use of
Excel to draw
graphs, graphs are
labelled with some
errors and relevant
to the question.
Basic use of Excel
to draw graphs,
graphs are partially
labelled and
partially relevant to
the question.
Poor use of Excel
to draw graphs,
graphs are have
no relevant labels
and are not
relevant to the
question.
No graphs
30 (Q1), 15 (Q2 & 3)
Communication
 Effective and relevant
 Logically sequenced
 Appropriate structure
 Use of mathematical, business
and English language
Exemplary logic,
structure and use of
mathematical,
business and English
language
Advanced logic,
structure and use of
mathematical,
business and English
language
Effective logic,
structure and use
of mathematical,
business and
English language
Satisfactory logic,
structure and use
of mathematical,
business and
English language
Unsatisfactory
logic, structure
and use of
mathematical,
business and
English language
No logic or
structure;
little use of
mathematical,
business and
English
language
20 (all Qs)
Conclusion (Questions 2 and 3)
• Clear relevant concluding
statement
• All questions answered
 Assumptions and limitation
addressed when called for
Clear statement of
conclusion with all
questions answered
appropriately;
excellent statement
of assumptions and
limitations when
required
Statement of
conclusion with
majority of questions
answered
appropriately; very
clear statement of
assumptions and
limitations when
required.
Statement of
conclusion with
questions
answered
appropriately; clear
statement of
assumptions and
limitations when
required.
Basic statement of
conclusion with
some questions
answered
appropriately;
sound statement of
assumptions and
limitations when
required.
Statement of
conclusion not
relevant to the
task.
Assumptions and
limitations
included but not
relevant
No conclusion
present
MATH1003 Assessment 3 S1 2022 3
Question 1: Using Indices and Compounding Interest (15% out of 45%)
A 21-year-old business graduate has just secured their first full time position and is aiming to save a
reasonable deposit to buy their first house. As such, the graduate must consider a savings strategy.
The graduate is aiming to have $125 000 saved over 6 years.
Task – Part 1
Using information given, determine the average rate of return required for the employee to reach
this savings target.
Useful Information
 As the graduate has been paying their university fees upfront, upon commencing their
position, they have an initial savings account balance (at age 21) of $8 000.
 The graduate’s current annual salary (at age 21, after tax) is $49 000, of which they can
contribute between 9.5% and 12% towards superannuation
 After making their superannuation contribution, the graduate’s living expenses must be
accounted for. During the first year, these amount to $25 000. In subsequent years,
expenses are assumed to increase by 3% each year. Anything left remaining after living
expenses represents potential savings to be put aside for the house deposit. In this instance,
the account that the graduate is depositing these savings into is a non-interest bearing
account (with a commencing balance of $8 000).
 The employee’s salary over the next 6 years is predicted to change as follows:
• At the end of Year 2, a pay increase of 1.25%
• At the end of Year 4, a pay increase of 2%
• At the end of Year 5, a final pay increase of 0.5%
Steps to help answer Part 1
a) Determine the graduate’s salary for each of the six years.
b) Determine the graduate’s superannuation contributions for each of the six years. For this section
you must pick your own value between 9.5% and 12% and use this value for all six years.
c) Determine the graduate’s living expenses for each of the six years. Then, from there, determine
the amount remaining that could be put towards a housing deposit per year over 6 years.
d) If the graduate does not reach their savings target at the end of 6 years, determine the time
required for the graduate to reach their savings goal if they were to place all of the savings
accumulated up to that point (i.e. by end of Year 6) into a ‘supercharge savings’ account which
accumulates interest compounded annually at 3.72%.
Task – Part 2
At the age of 27, due to circumstances beyond their control, the graduate is forced to withdraw
$20 000 back out from the account into which they have been depositing their savings account. The
graduate is then faced with a choice:
 Continue with their existing savings strategy, assuming (i) no pay rises beyond Year 6, (ii) no
change in superannuation contribution percentage and (ii) living expenses continue to increase
by 3% per year.
 Put the remaining balance into an interest-bearing account with a guaranteed return of 4.29%
per annum, compounding monthly.
MATH1003 Assessment 3 S1 2022 4
Steps to help answer Part 2
a) For maintenance of existing savings strategy, determine approximately how long it will take for
the account balance to reach $125 000.
b) For the interest-bearing account option, determine how long it would take the account balance
to reach $125 000.
c) Finally, finish with a conclusion summarizing the graduate’s final outcomes, with specific
reference to the value selected in step 2,the value obtained in steps 3 and 4 and a statement of
the impact of the $20 000 withdrawal at the end of Year 6.
MATH1003 Assessment 3 S1 2022 5
Question 2: Determining optimum profitability, output and employment (15% out of
45%)
Juanita operates a business that makes miniature sewing machines from a warehouse in an industrial
estate. Each machine costs them $99 to make and has additional fixed costs of $360 (per machine).
On average, Juanita sells 30 machines per week for a price of $120 each.
Juanita then decides to have a sale and reduces the price of each machine to an even numbered price
between $100 and $110 inclusive. During the sale, Juanita sells on average 54 machines per week.
Task
1. Select your own price value between $100 and $110 and determine the price-demand
function for this situation. HINT: Consider creating a pair of simultaneous equations.
2. Determine the Total Revenue function and Total Profit functions.
3. Determine Juanita’s break-even point(s). If there is more than one break-even point, what do
the values obtained represent?
4. Plot Total Cost, Total Revenue and Profit Functions on the same set of axes:
5. Find the Marginal Revenue (MR) and Marginal Cost (MC) functions by differentiation and
determine the level of output q at which MR = MC. With reference to your Excel plot, what
conclusion can you make about this value?
6. Confirm the maximum profit point (q) by differentiation in a way that proves that the point is
indeed a maximum. Also, confirm the amount of profit at that point by substitution.
7. The productivity of labour function for Juanita’s business is given by the equation
Q = 4.9√ – 0.86L. Juanita currently employs 12 workers. Determine
a. marginal productivity of labour for this number of employees and
b. the number of employees that would optimise productivity
8. Write a conclusion in which you summarise your interpretation of the results obtained.
a. Is the sale a viable proposition for Juanita based upon your calculations?
b. Is the current number of workers ideal for Juanita’s business?
c. State any underlying assumptions and limitations that could influence your
calculations and what might occur if these assumptions and limitations did not hold
firm over time.
MATH1003 Assessment 3 S1 2022 6
Question 3: Analysing sales figures using Statistics (15% out of 45%)
Two toy shops are known for their range of electric toy cars. As such, they sell reasonable numbers of
these cars over the course of a calendar year. Over a two-year period, the toy shop owners keep
records of car sales figures from month to month. During the first year, both toy shops sell a similar
combination of electric toy car models, but during the second year the second owner decides to
simplify the combination of electric toy cars sold and focus more upon the sale of slightly older
electric toy cars, for which spare parts are easier to obtain and also sell.
You are asked to analyse electric toy car sales figures from both toy shops, comparing sales
performance (i) between shops and (ii) between years.
Task
Analyse the provided sets of data from the two toy shops and make relevant comparisons using
appropriate measures of central tendency and spread.
Useful Information
The sales figures for the two toy shops over the two years are as follows:
Cars sold per month by Toy Shop 1 MONTH Cars sold per month by Toy Shop 2
Year 1 Year 2 Year 1 Year 2
54 49 ← January → 43 19
29 30 ← February → 31 33
49 31 ← March → 45 41
34 19 ← April → 18 23
26 8 ← May → 12 29
20 7 ← June → 5 22
9 14 ← July → 13 18
15 9 ← August → 7 29
61 50 ← September → 69 62
38 40 ← October → 32 84
42 33 ← November → 46 99
85 68 ← December → 79 73
Steps to help answer the question:
1. Calculate appropriate descriptive statistics for all sets of data (HINT: Consider Measures of
Spread and Measures of Central Tendency). Present full calculations showing how you obtain
each of your statistic values (except for Standard Deviation, for which you can use Excel).
2. Put these values into a table (one column for each set of data).
3. Using these statistics, construct appropriate plots which allow you to compare:
 Year 1 vs Year 2 sales for Toy Shop 1
 Year 1 vs Year 2 sales for Toy Shop 2
 Year 1 sales for Toy Shop 1 vs Toy Shop 2
 Year 2 sales for Toy Shop 1 vs Toy Shop 2
4. Write a Conclusion in which you interpret the results obtained and state – in your own words
– the impact of the change in sales strategy by the second toy shop owner. Note any
assumptions or limitations that could influence your results.

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