Topic: Operations Research

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  • 20 Marks

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.

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)

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  • 10 Marks

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

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

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)

 

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  • 10 Marks

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.

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)

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  • 1 Marks

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

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

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

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  • 1 Marks

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.

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

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  • 1 Marks

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

Identifies the components necessary for a linear programming problem.

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

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  • 10 Marks

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

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

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)

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  • 20 Marks

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

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

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)

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  • 1 Marks

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

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

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

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  • 1 Marks

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

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

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

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  • 20 Marks

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.

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)

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  • 10 Marks

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

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

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)

 

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  • 10 Marks

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.

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)

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  • 1 Marks

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

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

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

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  • 1 Marks

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.

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

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  • 1 Marks

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

Identifies the components necessary for a linear programming problem.

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

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  • 10 Marks

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

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

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)

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  • 20 Marks

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

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

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)

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  • 1 Marks

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

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

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

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  • 1 Marks

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

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

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

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