代写Quantitative methods for business 2024 Assignment 1代做Statistics统计

日期：2024-04-01 11:56

Question 1: Time Value of Money 32 Marks

a. Jasmine invests $5,000 in a savings account that earns an annual interest rate of 5% p.a., compounded monthly. How much will she have in the account after 5 years? (4 marks) How much interest could she earn? (1 mark) If she invests $5,000 in a flat rate account that yields 4% p.a., how many years are needed to achieve the same interest? (2 marks)

b. Joyce would like to gift her parents a cruise voucher valued at $9,800 for their coming wedding anniversary. However, she only has a part-time job with an income of $460 per fortnight. If she has a saving account which earns 3.8% p.a. compounded quarterly, how much does she need to deposit every quarter for the next one and a half years? (4 marks)

c. Alex, a small business owner, borrowed $78,000 to expand the business. The lender offers him a loan of 3 years with an interest rate of 7% p.a. compounding monthly. Help Alex with the following questions.

i. Calculate the minimum monthly repayment for Alex on this loan. (4 marks)

ii. Calculate the outstanding balance for Alex if there are only 3 months left. (2 marks)

iii. If Alex decides to make interest-only repayments for the first 6 months and then change to principal and interest repayments for the rest of the loan, use EXCEL to set up an Amortisation Schedule for him.  For full marks, show the calculations for “i” and “n” in adjacent cells (you can type these). Label each heading in Row 5 with your initials e.g.

“Period-sz”. (6 marks)

Hint: Use Excel formulae to compute the repayment size and to populate each value in the amortisation schedule

iv. Use your amortisation schedule from part (2) to calculate the total interest and the total amount paid over the life of the loan. Show your calculations for this amount using an appropriate Excel formula. (2 marks)

v. Discuss what could happen if the interest rate increased to 8% p.a after Alex has made 12 repayments. (2 marks)

d. Visit ‘Search for Real Estate, Property & Homes - realestate.com.au’ Enter your suburb and find your favourite property with a suggested price. Use the home loan calculator provided to estimate the repayment per month and insert the result to your Word document as below. (1 mark)

e. Use Excel to calculate the repayment for your favourite property if the interest rate is 6.19%. p.a. compounding monthly. Compare your answer with the website and discuss the difference.  (4 mark)

Question 2: Break-even Graphing 18 Marks

Jack has recently launched a new shop and would like to promote his business using the internet. He has prepared a 1-minute short video for his business and plans to advertise it on the following two websites:

• Comunikate has a fee of $35 per week for uploading and remaining the advertisement on the top page. If the number of clicks is less than 10,000, there is no extra charge. However, if the number of clicks exceeds 10,000, there will be an extra charge of $0.002 per additional click.

• LinkedIt has no weekly uploading and remaining fee, but charges according to the number of clicks as listed below:

number of clicks	Charges per click
0 to 6000	$0.001
6001 to 14000	$0.0015
more than 14000	$0.0025

a. Design an Excel table showing the costs of using these two websites. Assume that the number of total clicks is 40,000 per week. (5 marks)

b. Use any method to determine when the costs of using these two websites are equal. (3 marks)

c. Draw a line graph for the costs of using these two websites. Your graph is required to have the following:

• title of the graph with your ID number as part of the title. (2 marks)

• horizontal and vertical axis titles. (2 marks)

• the point that the costs are equal. (1 mark)

• the region that Comunikate is preferred. (1 mark)

• the region that LinkedIt is preferred. (1 mark)

d. Based on the calculation results, Jack negotiated a new rate with LinkedIt as below:

number of clicks	Charges per click
0 to 6000	$0.001
6001 to 14000	$0.0012
more than 14000	$0.0023

If he is expecting to receive 10,000 for the first week, which website he should choose? (3 marks)

Question 3: Linear Programming 25 marks

Jack, a hobbyist woodworker, specialises in making and selling 6-pack beer carriers, chopping boards and drink coasters at a local Sunday market. The production process requires the use of three primary resources: labour time, craft timber, and machine time. He is keen to spend a minimum of 300 minutes for labour and 200 minutes for machine time per week. However, he can only source a maximum of 300 lineal meter of timber per week due to limitations in storage. The requirements of each product are the following:

	Labour (min.)	machine time (min.)	Timber (meter)
beer carrier	4	2	2
chopping board	6	4	3
drink coaster	2	2	5

According to his sale history, Jack must produce a minimum of 20 beer carriers and 10 coasters, but a maximum of 14 chopping boards every week. The production cost for beer carrier, chopping board and drink coaster are for $25, $19, and $14 respectively.

Formulate a linear programming model for this problem to minimize the total production cost. In doing so, consider the following:

a. List the decision variables for this problem? (3 marks)

b. What is the objective for this problem? Using your decision variables, formulate the objective function. (2 marks)

c. What are the constraints in this problem? Using your decision variables, formulate these constraints (approximately 6) (6 marks).

d. Include the base Excel table with formulas, explanations, and the Answer Report and Sensitivity Report (6 marks)

Using the reports answer the following:

e. What is the optimal solution and minimum cost per week? (2 marks)

f. Which resources is not fully utilised and by what amount? (2 marks)

g. Can a new cost be calculated if all production costs dropped by $5? (2 marks)

h. Discuss and calculate the impact on cost if the machine time is reduced to 180 minutes. (2 marks)