NATIONAL OPEN UNIVERSITY OF NIGERIA

UNIVERSITY VILLAGE, PLOT 91, CASDASTRAL ZONE, NNAMDI AZIKIWE EXPRESS WAY, JABI, ABUJA.
FACULTY OF SCIENCES
SEPTEMBER 2020 EXAMINATION

COURSE CODE: CIT425

COURSE CREDIT: 3

COURSE TITLE: OPERATIONS RESEARCH

ALLOWED: 2 1 /2 HOURS

INSTRUCTION: ANSWER QUESTION ONE (1) AND ANY OTHER (4) QUESTIONS

1a. State the purpose of Operational Research, 2marks

1b. What are the Limitations of Operations Research 4marks

1c Explain the three components that make up LP model 3marks

1d what are the Properties of Linear Programming Model 4marks

1e Briefly explain the following concepts:

i.) Stage,

ii) state,

iii) forward and backward recursive approach 4marks

1f Differentiate between balanced and unbalanced transportation problems, and state what may lead to the unbalanced condition and how it may be handled. 5marks

2a. In which business areas may Operations Research be applied? 4 marks

b. Nigeria Coal Corporation (NCC) operates three mines in Enugu. The ore from each mine is separated into two grades before it is shipped. The daily production capacities of the mines, as well as their daily operating costs, are as follows:

NCC wants to deliver 50 tons of H-grade ore and 60 tons of L-grade ore by the end of the week. NCC pays employees’ full day's pay for each day or fraction of a day the mine is open. Compute the number of days each mine should operated during in a week if NCC is to fulfil its commitment at minimum total cost. 8marks 3a. Differentiate between these Models: i.) Static and Dynamic, ii.) Analytic and Simulation 4marks b. Peace Company transports refrigerator units from factories in Lagos and Onitsha to distribution centres in Abuja and Kano. Given the transport costs as in the table below, derive the linear programming model 8marks

The supply and demand, in number of units, is shown below:

4a. Write the steps taken to solve a linear programming (LP) problem graphically? 4marks b. Use the graphical method to find feasible and optimum solutions to the following problem 8marks Maximize: z = 5 x1 + 4 x2 Subject to: 6x1 + 4x2 ≤ 24 x1 + 2 x2 ≤ 6 - x1 + x2 ≤ 1 x2 ≤2 x1, x2 ≥ 0 (none negative values for the variables)

5a. Given the LP problem below: 7 ½ marks Maximize: z = 5 x1 + 4 x2 Subject to: 6x1 + 4x2 ≤ 24 x1 + 2 x2 ≤ 6 - x1 + x2 ≤ 1 x2 ≤2 x1, x2 ≥ 0 (none negative values for the variables)

i.) Use appropriate slacks to restate(write) the simplex form of the problem 2½ marks ii.) Set up the starting simplex table 2½ marks iii.) Without any computations write out the Basic and Nonbasic variables, and the solutions from the table from 2½ marks 5b. Write the steps followed to formulate the model of any optimization problem? 4½ marks 6a. Summarize the steps in formulation and solution of Dynamic Programming problems 5marks 6b. Write the algorithms for Vogel’s approximation method 7marks