# 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.