Reference no: EM132836850

MASC 0011 Quantitative Methods - Middle East College

Learning Outcome 1: Construct and solve Linear Programming models.

Learning Outcome 2: Make decisions under risk and uncertainty.

Assignment Objective

The aim of this assignment to test the understanding of the students in topics of linear programming and decision theory models. This assignment will test the knowledge of students in the allocation of scared resources and their decision making abilities on the basis of the mathematical computation.

Assignment Tasks

Question 1. Solve the following LPP problem graphically:

Minimize z = 2X₁ + 3X₂
Subject to 5X₁ + 10X₂ ≥ 90;           4X₁ + 3X₂ ≥ 48 ;             0.5X₁ ≥ 1.5 ; X₁, X₂ ≥ 0

What will be the impact on the solution if the objective function gets changed from minimization to maximization? Explain in your own words.

Question 2. Consider the following LPP:

Maximize Z = 3 x₁ + 2 x₂ + 5 x₃

Subject to x₁ + 2x₂ + x₃ ≤ 430,

3x₁ + 2x₃ ≤ 460,

x₁ + 4x₂ ≤ 420 with x₁, x₂, x₃ ≥ 0.

How many constraints and how many variables are there in the above LPP? What is the appropriate method to solve this LPP and why? Find the solution and hence interpret the result. (Note: The selected solution method should be from the learning outcomes of this module.)

Question 3. What are the different decision making environment that we had discussed? Explain any one decision- making process (except certainty) by giving suitable example. Interpret the result in your own words.

Question 4. Richard have been invited to play the Wheel of Fortune game on television. The wheel operates electronically with two buttons that produce hard (H) and soft (S) spin of the wheel. The wheel itself is divided into white (W) and red (R) half-circle regions. The wheel is designed to stop with a probability of 0.3 in the white region and 0.7 in the red region. The payoffs of the game are:

Alternatives	States of nature
		W (R.O.)	R (R.O.)
	H	Any     two/three-digit integer using the digits of your ID	Any three-digit integer using the digits of your ID

	S	Any three-digit integer using the digits of your ID	Any three-digit integer using the digits of your ID
	Probabilities	0.3	0.7

Draw the associated decision tree and specify the course of action.

Question 5. In the problem of Q4, what will happen to the decision-making environment if the probabilities are not given? Solve the reduced problem by using minimax regret criterion.

Question 6. This marks will be taken as the average of the marks obtained by the student in the In-Class activities/quizzes.

Attachment:- Quantitative Methods.rar