Reference no: EM133025315

MASC 20004 Quantitative Methods for Business - Middle East College

Learning Outcome 1: Construct and solve Linear Programming models.

Learning Outcome 2: Construct and test statistical hypothesis.

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 questions

1. ABC Company can produce three types of shirts T, V and P. Three kinds of threads are required for it, white, green and yellow threads. One unit length of type T shirt needs 5 + a yards of white thread and 3+b yards of green thread; one unit length of type V shirt needs 3+ a yards of yellow thread, 2+c yards of green thread and 2 yards of the white thread; and one unit length of type P shirt needs 6+c yards of green thread and 4+ a yards of yellow thread. The firm has a stock of only 10 yards of white thread, 18 yards of green thread and 15 yards of yellow thread. It is assumed that the income obtained from one unit length of type T shirt is 13 RO, of type V shirt is 15 RO and that of type P shirt is 24 RO. Formulate the problem as linear programming problem.

2. a. Solve the following Linear programming problem by using Simplex method:

Maximize Z = 2x₁ + 3x₂ + x₃ + 7x₄
Subject to constraints 8 x₁ + 3x₂ + 4x₃ + x₄ ≤ 6,
2 x₁ + 6x₂ + x₃ + 5x₄ ≤ 3,
x₁ + 4x₂ + 5x₃ + 2x₄ ≤ 7
x₁, x_2, x₃, x₄ ≥ 0. (20 marks)

b. Define linear programming model, and briefly explain its limitations and scope to various industries in your own words

3. Solve the following LPP problem using graphical method:

Minimize Z = bx + cy

Subject to the constraints

x + y ≤ 8
x ≤ 5
y ≤ 5
x + y ≥ 4
x, y ≥ 0

(Note: Draw the above problem in a graph sheet using black color pen and shade the optimal region. Upload the scanned image)

4. a. Assume that you are doing a research on people recovered from Covid -19 based the data of a particular agency. In this context define and briefly explain the following terms with suitable examples and assumptions.

(a) Null hypothesis

(b) Alternative Hypothesis

(c) Type -1 and Type 2 errors

(d) Critical region

(e) Confidence interval and level of significance

b. In Spring semester the average age of students attending VSR College was 23.7 years with a standard deviation of In Fall semester, in order to meet the needs of working students, more classes were scheduled during evening hours. A random sample of 75 students enrolled this semester was studied and found that the average age of these students was 20.1 years. Does the average age of the students at VSR College is decreased during this semester?

5. Airport authority of Qatar 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 is 40 mins. Random sample passengers, who used the Qatar Airport in a particular day, gave the following boarding time distribution.

Time taken to complete

the boarding process(mins) No of persons
0-10 a+2
10-20 b+3
20-30 5c+2
30-40 3d+3
40-50 e+15

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.