Master of Business Administration - Semester 2 Mb 0048: “Operations Research”
May 2012
Master of Business Administration - Semester 2
MB 0048: “Operations Research”
(4 credits)
(Book ID: B1301)
ASSIGNMENT- Set 1
Marks 60
Note: Each Question carries 10 marks. Answer all the questions.
Marks 60
1. (a) What is linear programming problem?
Ans: Linear programming (LP, or linear optimization) is a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model for some list of requirements represented as linear relationships. Linear programming is a specific case of mathematical programming (mathematical optimization).
More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints.
(b) A toy company manufactures two types of dolls, a basic version doll- A and a deluxe version doll-B. Each doll of type B takes twice as long to produce as one of type A, and the company would have time to make maximum of 1000 per day. The supply of plastic is sufficient to produce 1000 dolls per day (both A & B combined). The deluxe version requires a fancy dress for which there are only 500 per day available. If the company makes a profit of Rs 3.00 and Rs 5 per doll, respectively on doll A and B, then how many of each doll should be produced per day in order to maximize the total profit. Formulate this problem.
Ans.
Let X1 and X2 be the number of dolls produced per day of type A and B, respectively.
Let the A require t hrs.
So that the doll B require 2t hrs.
So the total time to manufacture X1 and X2 dolls should not exceed 2000t hrs.
Therefore, tX1 + 2tX2 ≤ 2000t
Other constraints are simple. Then the linear programming problem becomes:
Maximize p = 3 X1 + 5 X2
Subject to restrictions,
X1 + 2X2 ≤ 2000 (Time constraint)
X1 + X2 ≤ 1500 (Plastic constraint)
X2 ≤ 600 (Dress constraint)
And non-negatively restrictions
X1, X2 ≥ 0
2. What are the
Master of Business Administration - Semester 2
MB 0048: “Operations Research”
(4 credits)
(Book ID: B1301)
ASSIGNMENT- Set 1
Marks 60
Note: Each Question carries 10 marks. Answer all the questions.
Marks 60
1. (a) What is linear programming problem?
Ans: Linear programming (LP, or linear optimization) is a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model for some list of requirements represented as linear relationships. Linear programming is a specific case of mathematical programming (mathematical optimization).
More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints.
(b) A toy company manufactures two types of dolls, a basic version doll- A and a deluxe version doll-B. Each doll of type B takes twice as long to produce as one of type A, and the company would have time to make maximum of 1000 per day. The supply of plastic is sufficient to produce 1000 dolls per day (both A & B combined). The deluxe version requires a fancy dress for which there are only 500 per day available. If the company makes a profit of Rs 3.00 and Rs 5 per doll, respectively on doll A and B, then how many of each doll should be produced per day in order to maximize the total profit. Formulate this problem.
Ans.
Let X1 and X2 be the number of dolls produced per day of type A and B, respectively.
Let the A require t hrs.
So that the doll B require 2t hrs.
So the total time to manufacture X1 and X2 dolls should not exceed 2000t hrs.
Therefore, tX1 + 2tX2 ≤ 2000t
Other constraints are simple. Then the linear programming problem becomes:
Maximize p = 3 X1 + 5 X2
Subject to restrictions,
X1 + 2X2 ≤ 2000 (Time constraint)
X1 + X2 ≤ 1500 (Plastic constraint)
X2 ≤ 600 (Dress constraint)
And non-negatively restrictions
X1, X2 ≥ 0
2. What are the