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# The Essay Analyzes Bank Of England's Interest Rate, Microwave Oven Production Optimization, And Study Hours Vs Exam Results.

8 Pages / 1,942 Words Published On: 07-04-2021

## Bank of England lowers main interest rate to 0.25%

Question 1:
On the 4th of August 2016, the Bank of England (BoE) lowered its main interest rate to 0.25%, the lowest on record since the Bank has published rates in 1970, which still remains unchanged. As a consequence of this low level of rates, Virgin Money’s Lifetime Tracker Standard mortgage rate stands at 3.9%. Jeff Green is about to buy a house in the countryside which costs £650,000 and is taking out a 25-year repayment mortgage for 75% of the acquisition value of the house. Jeff has asked you to assess his ability to pay, in case the BoE increases its interest rate, as his maximum monthly payment cannot exceed £3,200. You are required to:
1. Calculate the monthly payment John will need to meet under current conditions.
2. Assess the effect on John’s monthly payments for each quarter percentage point increase in the BoE rate, up to 4% and identify at which rate Jeff would no longer be able to make the monthly payment.
3. Determine the shortest length (to the nearest month) of mortgage Jeff could take out if he wanted his monthly payment to be exactly the maximum he could afford (based on current mortgage assumptions).
Question 2:
A company that manufactures electrical appliances is looking at one of its lines (microwave ovens), where it offers three different levels of specification: Cheap which sells for £50, Average which sells for £100 and Premium which sells for £250. The production of each oven goes through four different stages and you have been provided with the following data table:
ProcessMachine Cheap Average Premium Cost per hour Max. Available
Forming 1 hours 1.5 hours 3 hours £4.50 4,500 hours
Machining 3.5 hours 7 hours 13 hours £6.25 17,500 hours
Assembly 0.5 hours 1.5 hours 3.5 hours £7.75 6,500 hours
Testing 0.5 hours 1 hours 2 ½ hours £10.00 4,750 hours
The marketing department has also done some market research and believes demand for each of the models is limited to 2,000 units of the basic model, 1,200 of the medium and 700 of the luxury. You are required to:
1. Formulate this problem as a linear program and use Excel’s Solver to arrive at a solution, identifying what is the maximum profit the company can achieve in the
microwave ovens product line.
2. How would your answer change if the following happened:
a. Maximum demand for Premium model was 1,000; OR
b. Maximum available Machining hours were 20,000.
3. Write a report with a recommended production and marketing plan for the company.
Question 3:
A statistician is trying to find whether there is a relationship between the number of hours of study and exam results, or whether exam results are random. The first part of his study was to generate random numbers of study hours and exam grades, which will
be compared to the actual results once the exams are written. The data randomly generated is given in the table below:
1 25 80.0 45 96.0
2 5 8.0 3 29.0
3 18 16.0 14 46.0
4 29 87.0 49 32.5
5 17 95.0 11 61.0
6 39 14.0 19 61.0
7 49 9.5 43 12.0
8 25 10.0 44 46.5
9 6 35.0 0 95.0
10 22 58.0 38 66.0
11 37 8.0 38 24.0
12 31 89.0 50 62.0
13 18 57.0 17 60.5
14 45 22.0 33 10.0
15 5 39.5 33 61.0
16 4 90.0 42 36.0
17 17 23.0 45 39.0
18 29 55.0 34 86.0
19 16 74.0 15 87.0
20 22 29.0 29 100.0
21 28 69.5 49 76.0
22 6 27.0 39 50.5
23 21 12.0 31 55.0
24 4 82.0 14 67.5
25 24 26.0 10 94.0
26 12 13.0 17 33.0
27 4 23.0 34 85.0
28 38 24.5 45 33.0
29 31 77.0 3 19.0
30 5 71.0 44 38.0
Required:
1. Summarise the distribution of expected grades for both exams, according to the data given.
2. Construct a 95% confidence interval for the exam marks for each of the subjects. Is there a significant difference between them?

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