Quantitative methods for business 2024 Assignment 1Statistics

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$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$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 uploadai 写Quantitative methods for business 2024 Assignment 1Statistics ding 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) WX：codehelp