Reference no: EM132797055

204KM Operational Research - Coventry University

Learning Outcome 1: Explain and apply various methods of data collection for diverse uses. Design, conduct, analyse, report and critically evaluate a small-scale sample survey.

Learning Outcome 2: Model a range of situations for analysis by OR methods. Solve a range of business decision problems using appropriate software, analyse the output, and interpret the results in context.

Learning Outcome 3: Explain the basic ideas behind a range of OR techniques and summarise their underlying assumptions, applications and limitations.

PRODUCTION CAPACITY TASK

An electronics firm AJ & Sons limited in Japan manufactures radio models A, B and C, which have profit contributions of $16, $30 and $50 respectively. Each radio must pass through 3 different manufacturing processes: assembly, testing & packaging.

Model A requires 4 hours for assembly, 2 hours for testing, and 1 hour for packaging. The corresponding figures for Model B are 5 hours on assembly, 4 hours for testing and 2 hours for packaging. Lastly Model C requires 8 hours assembly, 5 hours for testing & 3 hours for packaging.

During the forthcoming week the company has available 112 plant-hours for assembly, 160 plant-hours for testing, and 48 hours for packaging. The company wishes to formulate this production planning problem as a linear programming problem and maximise profit and they have consulted you to provide the services as Operational Research analyst.

Using all the information above you are expected to prepare and present a report covering all the question below;

REPORT QUESTIONS/MARK DISTRIBUTION

a) Introduce what Operational research is and how it is relevant to AJ's decision making. Identify what the objective of the problem is and write it as anequation?

b) Explain what a decision variable is? Identify and define the decision variables for AJ productionplanning.

c) What resources limit AJ's production? How much resources are used for the manufacturing of the three models of Radio. Identify constraints and represent them in equations form.

Formulate the above LP model in standard form with all relevant details in the report.

d) Determine the standard form of the LP model after slack variables have been added.

e) Explain why slack variables are introduced into the LP model in part(d).

f) Produce an initial tableau of the LP problem

g) Identify the pivot column and pivot row and give reasons for your choice. Identify the pivot element.

h) Find the optimum solution using the row transformation method of simplex algorithm.

i) What would be your recommendations for optimum production of the model products and how much AJ will make per week?

Attachment:- Operational Research.rar