Topic: Operations Research

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QTB – Nov 2014 – L1 – SB – Q3 – Operations Research

Calculate control levels for inventory, expected time for a project, and identify the critical path in a network diagram.

Question

a. Calculate the various control levels from the following data on a given inventory item:

Normal usage: 1,600 per day
Minimum usage: 1,000 per day
Maximum usage: 3,000 per day
Lead time: 16 – 20 days
EOQ: 40,000
(9 Marks)

b. If the optimistic, most likely, and pessimistic times are given as 11 days, 15 days, and 18 days respectively, calculate the expected time of the project delivery.
(3 Marks)

c. The network for a small building project is shown below together with the time in days required to complete each task.

Required:

i. List the possible paths together with their durations through the network. (6 Marks)
ii. State the critical path and the project duration. (2 Marks)

(Total: 20 Marks)

Answer

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Tags: Control Levels, Critical Path, Economic Order Quantity (EOQ), Expected Time, Network Analysis
Level: Level 1

Topic: Operations Research
Series: NOV 2014

QTB – May 2017 – L1 – SB – Q5a – Operations Research

Graph linear inequalities and identify the coordinates of the corner points of the shaded area.

Question

Given the following inequalities:

i. Graph them on the same graph sheet using the following scales: On x and y-axes, let 1 cm represent 250 units. (6½ Marks)

ii.

Shade the area in which these inequalities hold.
Determine the coordinates of the corner points of the above shaded area. (3½ Marks)

Answer

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Tags: Corner Points, Graphing, Linear Inequalities, Shaded Area
Level: Level 1

Topic: Operations Research
Series: MAY 2017

QTB – May 2017 – L1 – SB – Q4b – Operations Research

Identify non-basic variables in a transportation model and calculate the probability of a specific event in random disk selection.

Question

i. Given the following initial basic tableau of a transportation problem:

Identify the non-basic variables and compute their corresponding
relative cost coefficients. (4marks)

ii. A bag contains 39,800 white disks and 200 black disks from which
1,000 disks are taken at random. Calculate the probability that the
sample contains 4 black disks. (6marks)

Answer

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Tags: Non-basic Variables, Probability, Random Sampling, Relative Cost Coefficients, Transportation Problem
Level: Level 1

Topic: Operations Research
Series: MAY 2017

QTB – May 2017 – L1 – SA – Q20 – Operations Research

This question calculates the holding cost of a unit item based on EOQ and given parameters.

Question

In Inventory Control, the Economic Order Quantity (EOQ) of an item is given as 500 units, ordering cost as ₦500 per order, and the demand for the item in six months is 2,500 units. What is the holding cost of a unit of the item per annum?

A. ₦10
B. ₦20
C. ₦30
D. ₦40
E. ₦50

Answer

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Tags: Business operations, EOQ, Holding Cost
Level: Level 1

Topic: Operations Research
Series: MAY 2017

QTB – May 2017 – L1 – SA – Q19 – Operations Research

This question involves solving a transportation problem using the North-West Corner method to find the values of e+f.

Question

The tabulated information above shows the demands and supplies of a
transportation problem together with the unit costs of transporting. Use the
North-West method to find (e + f)

A. 83
B. 75
C. 66
D. 60
E. 55

Answer

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Tags: North-West Corner Method, Operations Research, Transportation Problem
Level: Level 1

Topic: Operations Research
Series: MAY 2017

QTB – Nov 2014 – L1 – SA – Q7 – Operations Research

Identifies the components necessary for a linear programming problem.

Question

The building blocks for a linear programming problem are:
A. A linear objective function and equality of constraints
B. A linear objective function and inequality constraints
C. A linear objective function, structural linear inequality constraints, and non-negativity constraints on the decision variables
D. A linear objective function, structural linear inequality constraints, and negativity constraints on the decision variables
E. A linear objective function and structural non-linear inequality constraints

Answer

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Tags: Constraints, Linear Programming, Objective Function
Level: Level 1

Topic: Operations Research
Series: NOV 2014

QTB – May 2016 – L1 – SB – Q6b – Operations Research

This question involves calculating seasonal adjustments based on moving average analysis for sales data.

Question

i. The following moving average analysis is obtained for the quarterly sales of a bakery based on the additive model:

Quarter	Trend	Actual Sales in the Quarter	Variation (Actual – Trend)
Year 1: Q3	29.375	29	-0.375
Year 1: Q4	33.125	33	-0.125
Year 2: Q1	37.125	37	-0.125
Year 2: Q2	41.250	41	-0.250
Year 2: Q3	45.000	46	1.000
Year 2: Q4	47.875	48	0.125
Year 3: Q1	53.000	51	-2.000
Year 3: Q2	57.125	58	0.875

Required:
Calculate the seasonal adjustment for each quarter.
(6 marks)

ii. An electrical bulb-making company runs a production line that contains 760 bulbs of the same wattage. These bulbs fail on a regular basis according to the following probability distribution:

Life (months)	Probability of Failure (P)
1	0.27
2	0.56
3	0.17

Required:
If the cost of replacing a bulb is N60, determine the following:

The life span (2 marks)
The average number of replacements in the period (1 mark)
The average monthly cost of replacing the bulbs. (1 mark)

Answer

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Tags: Forecasting, Moving Averages, Seasonal Adjustment
Level: Level 1

Topic: Operations Research
Series: MAY 2016

QTB – Nov 2015 – L1 – SB – Q6 – Operations Research

Formulate a linear programming problem for optimizing investment in conservative and speculative inventories under given constraints.

Question

Assume that the management of Community Bank Limited wants to invest up to N100,000 in inventory considered to be either conservative or speculative. The company’s board-approved investment policy is that the investment in conservative inventory should be at most N80,000, while the investment in the speculative inventory should be at least N12,000. Assume further that N1.6 return is expected on each naira invested in the conservative inventory, N2.0 return is expected on each investment in the speculative inventory, and that monetary policy regulations require that investment in the speculative inventory should be at most one-third of the investment in the conservative inventory.

Required:

a. State the type of Operations Research problem described above. (2 Marks)

b. Formulate mathematically the:

i. Objective function. (4 Marks)

ii. Constraint inequalities. (8 Marks)

iii. Investment problem. (6 Marks)

(Total: 20 Marks)

Answer

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Tags: Constraints, Inventory Management, Investment policy, Linear Programming, Optimization
Level: Level 1

Topic: Operations Research
Series: NOV 2015

QTB – May 2016 – L1 – SA – Q20 – Operations Research

Calculating traffic intensity or utilization factor in a simple queue given arrival and service rates.

Question

In a simple queue, if the arrival rate is 5 customers in 15 minutes and the service rate is 8 customers in 12 minutes. the traffic intensity or utilization factor is

A. 0.25
B. 0.50
C. 0.55
D. 0.65
E. 1.00

Answer

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Tags: Arrival Rate, Queuing Theory, Service Rate, Traffic Intensity
Level: Level 1

Topic: Operations Research
Series: MAY 2016

QTB – May 2016 – L1 – SA – Q19 – Operations Research

Expressing a production time constraint for two products given limited direct labour hours.

Question

A company makes two products X and Y. It takes 2¼ hours to make one unit of X and 3¾ hours to make one unit of Y. If only 18,000 direct labour hours are available, then the production time constraint is expressed as

A. 3.75x + 2.25y ≤ 18,000
B. 2.25x + 3.75y ≤ 18,000
C. 3.75x + 2.25y ≥ 18,000
D. 2.75x + 3.75y ≥ 18,000
E. 3.75x + 2.25y = 18,000

Answer

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Tags: Linear Programming, Production Constraints, Time Management
Level: Level 1

Topic: Operations Research
Series: MAY 2016

QTB – Nov 2015 – L1 – SB – Q2b – Operations Research

Determine the level of output that minimizes the average cost for a given total cost function.

Question

MANDILAS Ventures has established its total cost function to be:

Determine the level of output that will give minimum average cost. (8 Marks)

Answer

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Tags: Average Cost, Cost Analysis, Output Level, Total Cost Function
Level: Level 1

Topic: Operations Research
Series: NOV 2015

QTB – May 2015 – L1 – SB – Q6 – Operations Research

This question involves calculating the change in revenue, total revenue, total cost, and total profit for a manufacturer based on given marginal cost and marginal revenue functions.

Question

A manufacturer determines that the firm’s Marginal Cost (MC) and Marginal Revenue (MR) functions are:

MR = R′(x)=100 + 0.1x

You are required to find the:

a. Change in revenue that results when the sales level increases from 20 to 30 units. (5 Marks)
b. Revenue resulting from the sale of 30 units. (5 Marks)
c. Cost of producing 30 units if the fixed cost (at $x = 0$ ) is N400. (5 Marks)
d. Total profit when 30 units of the product are sold. (5 Marks)

Answer

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Tags: Fixed Cost, Marginal Cost, Marginal Revenue, Profit, Total Revenue
Level: Level 1

Topic: Operations Research
Series: MAY 2015

QTB – May 2015 – L1 – SB – Q4 – Operations Research

This question requires calculating the average machine life, replacement costs, and determining the best replacement strategy for ATM machines in a bank.

Question

The management of a bank observed that the disruption of the bank ATM services was due to the age of the machines. Data on ATM failure is as follows:

Year after replacement	1	2	3
Cumulative % of failures	30%	75%	100%

It was further observed that 1,000 units of these machines are in use nationwide and they can be replaced collectively for N5 million per machine. If replaced individually, they cost N30 million per machine.

You are required to calculate:
a.
i. Average machine life (2 Marks)
ii. Average number of replacements per year (2 Marks)
iii. Cost of individual replacement per year (2 Marks)
iv. Cost of mass replacement at the end of the year (12 Marks)

b. Determine the best replacement strategy (2 Marks)

Answer

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Tags: ATM Services, Cost Analysis, Machine Life, Replacement Theory, Strategy
Level: Level 1

Topic: Operations Research
Series: MAY 2015

QTB – Nov 2015 – L1 – SA – Q8 – Operations Research

This question asks about the simulation method that uses random numbers to predict system behavior.

Question

A simulation method that uses random numbers to predict system behavior is called:

A. Markov chain simulation
B. Box Jenkins simulation
C. Random variable simulation
D. Stochastic simulation
E. Monte Carlo simulation

Answer

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Tags: Monte Carlo Simulation, Simulation, System Behavior
Level: Level 1

Topic: Operations Research
Series: NOV 2015

QTB – Nov 2015 – L1 – SA – Q7 – Operations Research

This question identifies which factor does not affect the optimal replacement interval for an asset.

Question

If an asset can be replaced at the same cost and there is no time value of money, then the problem of obtaining the optimal replacement interval involves the following EXCEPT:

A. Finding the cumulative operating/maintenance cost
B. Finding the total depreciation
C. Adding (A) and (B) above to get total cost
D. Finding the year at which marginal cost is minimized
E. Finding the year at which average cost is minimum

Answer

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Tags: Average Cost, Cost Analysis, Marginal Cost, Replacement Theory
Level: Level 1

Topic: Operations Research
Series: NOV 2015

QTB – May 2015 – L1 – SB – Q3a – Operations Research

Determining the equilibrium price and quantity from demand and supply functions.

Question

A producer wishes to determine the equilibrium price and quantity of his goods in the
market. He estimated the market demand and supply functions as follows:

where P is the price in thousands of naira and q is quantity in thousands of units, calculate
the equilibrium price and quantity for the producer

Answer

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Tags: Demand, Equilibrium, Price, Quantity, Supply
Level: Level 1

Topic: Operations Research
Series: MAY 2015

QTB – May 2015 – L1 – SA – Q13 – Operations Research

Identifying the meaning of the acronym EOQ in inventory control.

Question

The acronym EOQ in inventory control system stands for:

A. Economic Order Quantity
B. Economic Optimal Quantity
C. Equilibrium Optimal Quantity
D. Economic Ordering Quality
E. Equilibrium Ordering Quality

Answer

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Tags: Cost Minimization, Economic Order Quantity, Inventory Control
Level: Level 1

Topic: Operations Research
Series: MAY 2015

QTB – May 2015 – L1 – SA – Q6 – Operations Research

Finding revenue changes, total cost, and profit using marginal cost and marginal revenue functions.

Question

In its efforts to reposition the fortune of the firm, the Board of Directors of AJE Enterprise Limited targeted a profit function of . The firm’s profit-maximizing output level is obtained as:

A. 2/5
B.
C. 8
D. 10
E. 16

Answer

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Tags: Maximization, Output Level, Profit Function
Level: Level 1

Topic: Operations Research
Series: MAY 2015

QTB – May 2015 – L1 – SA – Q5 – Operations Research

Identifying marginal productivity functions for labor and capital in a given production function.

Question

ABC Plc announced at its AGM in March 2014 that its production function for the year 2013 was $Q=5L^0.4K^0.6Q =$ , where is the output level, $L$ is the labor input, and $K$ is the capital input. Therefore, the marginal productivity functions for both and $K$ are respectively given as:

Answer

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Tags: Capital Input, Labor Input, Marginal Productivity, Production Function
Level: Level 1

Topic: Operations Research
Series: MAY 2015

QTB – May 2015 – L1 – SA – Q4 – Operations Research

Understanding when a business venture is considered worthwhile.

Question

A business venture is considered as worthwhile when the:

A. Present value of revenue is positive
B. Present value of the cost is positive
C. Net present value is positive
D. Net present value is equal to zero
E. Internal rate of return is positive

Answer

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Tags: Internal Rate of Return, Net Present Value, Present Value
Level: Level 1