SMU MB0048 SET 1 SOLUTION

Q.1. 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 facny dress of ehich 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 maximise the total profit. Formulate this problem.

A.1

Answer:

Formulation maximize z =3x₁ +5x₂

Constraints  x₁+2x₂<=2000

X₁+x₂<=1500

X₂<=600

X₁,x₂>=0

[x₁=1000,x₂=500,max z= 5500]

Q.2. What are the advantages of Linear programming techniques?

A.2  Advantages of Linear Programming

1.The linear programming technique helps to make the best possible use of available productive resources (such as time, labour, machines etc.)

2. In a production process, bottle necks may occur. For example, in a factory some machines may be in great demand while others may lie idle for some time. A significant advantage of linear programming is highlighting of such bottle necks.

Q.4.What is integer programming?

A.4 An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming, which is also known as mixed integer programming when some but not all the variables are restricted to be integers.

Integer programming is NP-hard. A special case, 0-1 integer linear programming, in which unknowns are binary, is one of the Karp's 21 NP-complete problems. However, integer programs with a constant number of variables may be solved in linear time as an LP-type problem.[1][2] In variable dimension, iterative methods using the Graver basis of the matrix defining the system, enable the solution of broad classes of linear and nonlinear integer programming problems in polynomial time [3], and provide a parametrization of all integer programming problems.

Q.5 Explain the different steps involved in simulation methodologies?

A.5 

1. Define an achievable goal

2. Have a complete mix of skills in the team

3. Use modern tools and techniques of S/W development

4. Select the proper simulation language

5. Involve the end-user

6. Provide on-going documentation

7. Verify and validate the model

Q.6. Write down the basic difference between PERT &CPM.

A.6

PERT (Program Evaluation and Review Technique)	CPM (Critical Path Method)
1)PERT is a probabilistic tool used with three	1)CPM is a deterministic tool, with only single Estimating the duration for completion of estimate of duration activities.
2)This tool is basically a tool for planning	2)CPM also allows and explicit estimate of and control of time. costs in addition to time, therefore CPM can  control both time and cost.
3)PERT is more suitable for R&D related	3)CPM is best suited for routine and those projects where the project is performed for projects where time and cost estimates can the first time and the estimate of duration be accurately calculated are uncertain.
4)The probability factor i major in PERT	4)The deterministic factor is more so values or so outcomes may not be exact. outcomes are generally accurate and realistic.