Reference no: EM132600766
MASC20004 Quantitative Methods for Business - Middle East College
Learning Outcome 1: Construct and solve Linear Programming models.
Learning Outcome 2: Construct and test statistical hypotheses.
Assignment Objective
1. To test the understanding and application of Mathematical concepts learning.
2. To test the calculation skills and Mathematical modelling ability of the learner.
3. To test the knowledge acquired by the learners on using statistical test and ability to infer on the outcomes.
Assignment Tasks
Use the suitable resources to find the solution of the following problems.
Assignment questions
Question 1. Explain how you plan your study time (in minutes) to maximize your GPA of this semester by using linear programming. Assume that you have register for atleast 3 modules and all the modules are having equal credits. Plan your daily online class time, self-study time, personals routine times and office time (if you are working). Explain( both as verbal and symbolic) details of all variables you are assuming and meaning of all inequalities formed. Make sure the data are realistic and smart. Explain the whole process in not less than 300 words.
Question 2. Solve the following problem using graphical method. Show all the feasible solutions and obtain the optimal solution of the problem. Assume the questions represented below is a situation of a buyer in a shopping mall, interpret the answers x1, x2 a??d z in your own words not less than 50 words. (Follow the "Instructions to students" to replace a,b,c,d,e,f & g by its values)
min z = ax1 + gx2
Subject to the constraints that
ax1 + cx2 ≥ 15+b
dx1 + 2cx2 ≤ 45+b
ex2 + fx2 ≤ 80+b
x1, x2 ≥ 0.
Question 3. Solve the following linear programming problem by using simplex table method.
MAX z = 15x1 - 3x2 - 7x3
subject to
3x1 - 5x2 + 2x3 ≤ 72
4x1 + 7x2 + 9x3 ≤ 100
-12x1 + 4x2 + 5x3 ≤ 290
a??d x1, x2, x3 ≥ 0 .
Question 4. Assume that you are planning to buy a car in the used cars market. Explain the procedure how you will best fix the price. How many cars you will check? What is the best test statistics you will choose to test your hypothesis? Assume the company XYZ is offering the same brand car what you are looking for at a cost of 5000 rials. Will you accept the price or not? Assume that all cars in used cars market are approximately at same condition. What is your null and alternate hypothesis? What is your possible negotiation limit? Is it a one tail or two tail test? Explain the whole process of making decision statistically in 300-500 words.
Question 5. Airport authority of MADRAS claims that the average time taken by their passengers to complete the boarding process is less than the average of all other Airports in the country 60 mins. A random sample passengers, who used the Madras Airport in a particular day, gave the following boarding time distribution. (Follow the "Instructions to students" to replace a,b,c,d,e & f by its values)
Calculate the arithmetic mean and standard deviation of this distribution and use these values to test their claim at 5% level of significance. Comment their claim based on your investigation.
Question 6. The mean time taken to submit an assignment by a student was 20 days according to the previous semester record. The Exam office claimed that this year the submission time increased due to the natural calamities. Was the submission time really increased or not. Test the hypothesis with a 5% level of significance. The time taken by 15 students to submit their assignment are given below (14+a), (15+b),(16+c),(17+d),( 18+e) ,19, (20+a), (21+b), (22+c), (23+d),(24+e),(25+f), (26+a),(27+b), (28+c). (Follow the "Instructions to students" to replace a,b,c,d,e & f by its values)