Question 1
Household Tools Co. is a manufacturer of microwave ovens. The manufacturer wants to increase the shelf life of their products. Past records indicate that the average shelf life of their microwave ovens is 240 days. After a new line of microwave ovens has been developed, a sample of nine boxes of this product shows the following shelf lives (in days):
235, 247, 258, 269, 226, 237, 227, 268 and 278
At the 0.05 level, the manufacturer wants to test if the shelf life of the microwave oven increased.
a) What are the null and alternative hypotheses of the test?
b) Determine the decision rule for the test.
c) Calculate the p-value of the test. What is the manufacturer's conclusion?
Question 2
A shipping economist studies the relationship between the value per tonne of containerised cargo (x) and the freight rate charged by shipping lines for a same shipping route (y). The following table shows the values of x and y for ten shipments:
|
x
|
1000
|
2200
|
1800
|
2500
|
4050
|
3600
|
4000
|
4000
|
4500
|
6500
|
|
y
|
250
|
265
|
240
|
220
|
280
|
260
|
275
|
265
|
285
|
275
|
a) Develop the least squares regression line to study the relationship between x as the independent variable and y as the dependent variable.
b) Conduct a hypothesis test to see if cargo value has any positive impact on the freight rate.
c) Evaluate the performance of the linear regression model and suggest how it can be improved.
Question 3
King Kong Furniture is a furniture manufacturer of desks and chairs. Each chair sold yields a profit of $25, and each desk sold yields a profit of $55. Marketing restriction requires that the number of chair produced be at least twice the number of desks produced. There are 100 units of wood available. Each chair uses 4 units of woods, and each desk uses 8 units of woods. Let X and Y be the numbers of chairs and desks that the manufacturer produces respectively.
a) Develop a linear programming problem in terms of the production function and constraints, in order to maximise the manufacturer's total profit.
b) Use Excel Solver to solve the above linear programming problem. Comment on the Excel Solver's results.
Question 4
The Shipping & Logistics Department of a university wants to decide which of the two magazines, Containerisation International or Lloyd's Shipping Economist, should be used to advertise its new Bachelor of International Logistics program.
a) What quantitative method can be applied to help the department to make the decision? In a few paragraphs, explain how this method can be applied.
b) In a few paragraphs, explain how a qualitative method can also be applied to help the department to make the decision.