Question 1 (Total of 12 marks)
On Marys 16th birthday, her parents invest on her behalf an amount of $4,000 into an account that pays interest at 3.8% compounded semi-annually.
(5 marks) How much will the account be worth on Marys 21st birthday?
(7 marks) Would Mary be better off if the account paid interest at 3.75% compounded quarterly? Explain.
Question 2 (Total of 12 marks)
Luxury Rides Taxi Service must replace cars every 5 years at a cost of $450,000. The company is considering depositing $4,000 at the end of each month at 8% per year compounded monthly. Confirm your answer using EXCEL. Will they meet the target with this strategy? Explain. If your answer is no, what size deposits should they be making instead?
Question 3 (Total of 24 marks)
Kate and Miles are shopping for a new home. They can afford a down payment of $60,000 and monthly payments of at most $2,500.
(7 marks) Sterling Bank has offered to finance a loan at 8.75% per year compounded monthly for 30 years. What is the most expensive house (to the nearest dollar) they can afford to buy?
(6 marks) Kate and Miles ultimately make a downpayment of $50,000 on a $300,000 home and finance the balance through Creative Financing Inc. at 8.25% per year compounded monthly for 30 years. What monthly payments should Kate and Miles make to pay off the house?
(8 marks) Referring to part (b), use EXCEL to set up an Amortisation Schedule for the first 12 months of the loan. Attach the printout or copy your EXCEL amortisation into your assignment submission.
EXCEL Instructions: Please refer to the amortisation example in Week 3 lecture notes and Topic 3 in the EXCEL Booklet.
(3 marks) Referring to the Amortisation Schedule from part (c), how much interest in total will Kate and Miles pay over the first year of their loan? How much equity (downpayment plus repaid principal) in the house will they have at the end of the first year?
Question 4 (Total of 24 marks)
Hit-and-Miss Airlines are considering providing a new daily service between two cities. The aircraft has a maximum capacity of 200 passengers and each flight incurs a fixed cost of $27,000 regardless of the number of passangers. In addition, a cost is also incurred of $75 per passanger to cover such things as catering, booking, baggage handling.
(12 marks) The company is thinking of charging $225 per ticket. How many passengers will the airline need on each flight to break even? Find the break-even point algebraically and illustrate it using an EXCEL graph. Attach the printout or copy your EXCEL graph into your assignment submission. Based on your analysis, will Hit-and-Miss realize a profit or a loss if 160 seats are sold for a particular flight? Explain briefly.
EXCEL Instructions: Create a column called Number of Passengers and in that column enter values from 0 to 200 in increments of 20. Then create two more columns, one for Total Cost and another for Total Revenue. Enter appropriate formulae in EXCEL to obtain the total cost and total revenue corresponding to each value in the Number of Passengers column. Highlight the resulting three sets of numbers and go to the Chart Wizard to obtain the graph. Make sure that your graph has been labelled appropriately (i.e. title, axis labels, legend). Please refer to Topic 3 in the EXCEL Booklet for further instructions on entering formulae and graphing in EXCEL.
(6 marks) Hit-and-Miss Airlines know from previous experience that they are unlikely to sell more than 80 percent of seats on any one flight. Assuming they sell exactly this many, what price per seat should they charge to break even?
(6 marks) The company also has the option of accepting a cargo contract. Under this contract, the airline will receive $5,000 per flight for transporting cargo but, because of the extra weight, it will have to reduce its maximum number of passengers to 180. Find the new break-even ticket price for a full flight.
Question 5 (Total of 28 marks)
Joe Bright, the marketing manager for Mountain Mist soda needs to decide how many TV spots and magazine advertisements to run during the next quarter. Each TV spot costs $5,000 and is expected to increase sales by 300,000 cans. Each magazine advertisement costs $2,000 and is expected to increase sales by 500,000 cans. The total soda advertising budget for the next quarter is set at $100,000; however Mountain Mist wants to spend no more than $70,000 on TV spots and no more than $50,000 on magazine ads. Mountain Mist earns a profit of 5 cents on each can of soda it sells. Joe has decided to use linear programming to find the most profitable mix of advertisements. He asks for your help.
(1 mark) What are the decision variables for this problem?
(3 marks) Using decision variables identified in part (a), formulate the objective function for this problem. Is the quantity of interest to be maximized or minimized?
(2 marks) What is the limited resource in this problem? Using decision variables from part (a), formulate the constraint for this resource.
(2 marks) What other constraints are relevant to this problem? Using the decision variables from part (a), formulate those constraints.
(4 marks) Use EXCEL Solver to obtain a solution to the linear programming problem from part (e), together with an Answer Report and a Sensitivity Report. Provide a printout of your EXCEL spreadsheet and of the two Excel reports with your assignment submission.
EXCEL Instructions: All EXCEL output should bear your e-mail ID. To ensure this, you will need to save your EXCEL file as E-mail ID Advertising Plan.xls. In addition, your constraint names should begin with your initials, e.g. JB_Budget.
Please refer to Topic 5 in the Excel Booklet or the Linear Programming Supplement to the textbook (pdf file posted on the course website) for detailed instructions on how to set up your spreadsheet and use Solver.
(6 marks) Mountain Mists major competitor has just launched its new TV advertising campaign. Joe worries that Mountain Mists TV spots will be less effective and only increase sales by 200,000 cans. Would the solution obtained in part (f) still be optimal? Which of the EXCEL reports helps you answer this question? Justify your answer carefully. How would Mountain Mists total profit change, if at all?
(4 marks) Prepare a report that summarizes linear programming results. Your report should discuss the following issues:
The optimal number of TV spots and magazine advertisements and the maximum increase in profit next quarter.
The actual cost of Mountain Mists advertising and the amount left in the budget, if any.
The total cost of the optimum number of TV spots, and of the magazine advertisements.
Which report enables you to answer these questions?
(6 marks) What is the impact on the maximum profit if the budget is increased by $10,000.
Include in your answer a discussion of the shadow price.