Unity University
MBA Program
Assignment Guideline for the course Quantitative Methods for Decision Making
Expected date of Submission: February 6/2022
Total point allotted: 25%
Objective of the Assignment
The basic objective of this assignment is to enable students to practice what they have
learnt in the class in solving the problems given as a group assignment using graphical and
simplex methods.
General Guideline
Make a group of 8 individuals/students and try to solve the linear programing problems
(LPP) given as assignment following the requirements of the particular LPP. Try to show
all the necessary steps for the solutions of the LLP.
1) 3F manufacturer produces two products: Beds and Chairs. Each unit of Bed requires
3 hrs in molding unit, 4hrs in painting unit, and 1 hr in finishing. On the other hand,
each unit of Chair requires 3 hrs in molding unit, 2 hrs in the paint shop and 2 hours in
finishing. Each week, there are 210 hrs available in molding, 200hrs in painting, and
120 hrs in finishing unit. The demand for Beds cannot exceed 40 units per week. Each
unit of Bed contributes Birr 20 to profit, while each unit of chair contributes Birr 30.
Determine the number of units of each product per week to maximize the profit?
A) Formulate LP Model showing the necessary steps.
B) Solve the LLP using graphical approach.
C) How many units of each product has to be produced?
D) What is the maximum profit?
2) A firm produces three products A, B, and C. Each of these products passes through three
departments: Fabrication, Finishing, and Packaging. Each unit of product A requires 3,
4, and 2 hours respectively in the three departments. Each unit of product B requires 5, 4,
and 4 hours respectively in the three departments. Each unit of product C requires 2, 4, and
5 hours respectively in the three departments. Every week, 60 hours are available in the
Fabrication department, 72 hours in the Finishing department, and 100 hours in the
Packaging department. The firm sells each unit of products A, B, and C for $10, $20, and
$16 respectively. The cost of production per unit for products A, B, and C are $5, $10, and
$8 respectively.
Required:
i) Formulate the problem as a LPM
1
ii) Using simplex method determine the number of units of each of the three
products that the firm should produce each week so as to maximize the
total profit.
iii) How much is this maximum profit?
iv) Determine if any capacity would remain unutilized
3) Min Z = 12X1+20X2
Subject to:
6X1 + 8X2 ≥100
7X1 + 12X2 ≥120
X1, X2 ≥ 0.
A) Solve the LLP using graphical approach.
B) How many units of each product has to be produced?
C) What is the minimum cost?
4) A company has two plants, each of which produces and supplies two products: A and
B. The plants can each work up to 16 hrs a day. In plant 1, it takes 3 hrs to prepare and
pack 1000 gallons of A and 1 hr to prepare and pack 1 quintal of B. In plant 2, it takes 2
hrs to prepare and pack 1000 gallons of A and 1.5 hrs to prepare and pack a quintal of B.
In plant 1, it costs Birr 15,000 to prepare and pack 1000 gallons of A and Birr 28,000 to
prepare and pack a quintal of B, whereas these costs are Birr 18,000 and Birr 26,000
respectively in plant 2. The company is obliged to produce daily at least 10,000 gallons of
A and 8 quintals of B.
i) Formulate the problem as LPM to find out as to how the company should
organize its production so that the required amounts of the two products be
obtained at minimum cost.
ii) Solve the problem using simplex method.
iii) What is the minimum cost?
