Answer to MTP_Intermediate_Syllabus 2012_Dec2013_Set 1 Directorate of Studies, The Institute of Cost Accountants of India (Statutory Body under an Act of Parliament) Page 1 Paper 9 - Operations Management and Information Systems Section –A [Question no. 1 is compulsory and any 4 from the rest] 1 Answer the following questions: (a) A work sampling study is to be made of a typist pool. It is felt that typists are idle 30 percent of the item. How many observations should be made in order to have 95.5% confidence that accuracy is within ±4%. (b) A steel plant has a design capacity of 50,000 tons of steel per day, effective capacity of 40,000 tons of steel per day and an actual output of 36,000 tons of steel per day. Compute the efficiency of the plant and its utilization. (c) The demand function of a firm is q = 200 – 10p and the average cost function is . 25 q 10 AC If the firm’s objective is to maximize profit, what will be its profit maximizing output? (d) Consider the pay off matrix given below: Player B λ 6 2 2 B B A A A Player 2 1 2 1 (i) Show that whatever be the value of λ , the game is strictly determinate. (ii) Determine the value of game (e) If a firm sells 8,000 units, its loss is ` 20,000. But if it sells 10,000 units, its profit is ` 20,000. Calculate Fixed Cost. (f) List the name of the Qualitative Approaches regarding the Forecasting Technique. [6x2] Answer of 1: (a) Number of observations required for Work sampling study 2 2 E pq C N Where C = constant depending on confidence level p = percentage of idling; q = percentage of activity; E = error C = 2 for 95.5% confidence level; p = 0.3 ; q = 1 – p .= 0.7 ; E = ±4% 525 0016 . 0 84 . 0 ) 04 . 0 ( 7 . 0 3 . 0 4 N 2 (b) Efficiency of the plant = Actual output/ Effective Capacity = (36,000 /40,000) x100 =90%
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Answer to MTP_Intermediate_Syllabus 2012_Dec2013_Set 1
Directorate of Studies, The Institute of Cost Accountants of India (Statutory Body under an Act of Parliament) Page 1
Paper 9 - Operations Management and Information Systems
Section –A
[Question no. 1 is compulsory and any 4 from the rest]
1 Answer the following questions:
(a) A work sampling study is to be made of a typist pool. It is felt that typists are idle 30
percent of the item. How many observations should be made in order to have 95.5%
confidence that accuracy is within ±4%.
(b) A steel plant has a design capacity of 50,000 tons of steel per day, effective capacity
of 40,000 tons of steel per day and an actual output of 36,000 tons of steel per day.
Compute the efficiency of the plant and its utilization.
(c) The demand function of a firm is q = 200 – 10p and the average cost function is
.25
q10AC If the firm’s objective is to maximize profit, what will be its profit
maximizing output?
(d) Consider the pay off matrix given below:
Player B
λ
6
2
2
BB
A
AAPlayer
21
2
1
(i) Show that whatever be the value of λ , the game is strictly determinate.
(ii) Determine the value of game
(e) If a firm sells 8,000 units, its loss is ` 20,000. But if it sells 10,000 units, its profit is ` 20,000.
Calculate Fixed Cost.
(f) List the name of the Qualitative Approaches regarding the Forecasting Technique. [6x2]
Answer of 1:
(a) Number of observations required for Work sampling study 2
2
E
pqCN
Where C = constant depending on confidence level
p = percentage of idling; q = percentage of activity; E = error
C = 2 for 95.5% confidence level; p = 0.3 ; q = 1 – p .= 0.7 ; E = ±4%
5250016.0
84.0
)04.0(
7.03.04N
2
(b) Efficiency of the plant = Actual output/ Effective Capacity
= (36,000 /40,000) x100 =90%
Answer to MTP_Intermediate_Syllabus 2012_Dec2013_Set 1
Directorate of Studies, The Institute of Cost Accountants of India (Statutory Body under an Act of Parliament) Page 2
Utilization = Actual Output/Design Capacity
= (36,000/50,000) x 100 = 72% (c) Here the equation of the demand curve is
q = 200 – 10 p
or, 10 p = 200 – q
or, 2q10
120
10
q200p
So, total revenue (R) = pq = 20q - 2q10
1
Marginal Revenue (MR) q5
120
dq
dR
Again, AC = 10 + 25
q
Total Cost (C) = AC x q = 10q + 25
q2
Marginal Cost q25
210
dq
dc
Now, the first order condition for profit maximization requires, MR =MC.
20 - q25
210q
5
1
or, 1020q25
2q
5
1
or, 7
250
7
2510q10q
25
7
The second order condition requires that slope of MC>Slope of MR.
Now, slope of MR=
5
1
dq
MRd < 0 and slope of MC=
0
25
2
dq
MCd .
So, the second order condition is fulfilled.
Hence, to get maximum profit, the firm will produce 7
250units of output.
(d) (i) We determine the maximin and the minimax value, ignoring λ .
Player B
6
2
2
r
2
λ
6
2
2
BB
c
A
AAPlayer
21
2
1
Here maximin value = 2 and minimax value = 2. Thus, maximin value = minimax value.
So, whatever be the value of λ , the game is strictly determinable.
(ii) The value of the game is 2 to player A and – 2 to player B. The optimum strategy for A
is A1 and the optimum strategy for B is B1 . The Saddle point = (A1, B1).
(e) Change in quantity (10,000 – 8,000) units = 2,000 units Change in profit =` [20,000 – (-20,000)] = `40,000.
Answer to MTP_Intermediate_Syllabus 2012_Dec2013_Set 1
Directorate of Studies, The Institute of Cost Accountants of India (Statutory Body under an Act of Parliament) Page 3
Unit contribution = Output in Change
Profit in Change =
000,2
000,40`= ` 20
So, when output = 10,000 units Total contribution= (` 20 x 10,000) = ` 2,00,000
We know Contribution = Fixed Cost + Profit
2,00,000 = Fixed Cost + 20,000
or, 2,00,000 – 20,000 = Fixed Cost
or, Fixed cost = 1,80,000
(f) Qualitative approaches include five forecasting techniques:
Grass – Root Forecasting
Focused Forecasting
Historical Analogy
Panel Consensus
Delphi Method
2 (a) At Dr. Prachi’s clinic patients arrive at an average of 6 patients per hour. The clinic is
attended to by Dr. Prachi himself. Some patients require only the required prescription.
Some come for minor checkup while some others require through inspection for the
diagnosis. This takes the doctor 6 minutes per patient on an average. It can be
assumed that arrivals follow a Poisson Distribution and the Doctor’s inspection time
follows an Exponential Distribution.
Determine:
(i) The percentage of time that a patient can walk to the doctor without having to
wait;
(ii) The average number in the system.
(iii) The average number in the queue.
(iv) The average waiting time / unit in the system.
(b) Describe the role of Project Manager [7+5]
Answer of 2
(a) Here, λ = Mean arrival rate per unit of time=6 Patients per hour
μ = Mean service Rate per unit of time= 60x6
1 = 10 Patients per hour
(i) The probability that a patient can walk to a doctor without waiting or the
probability of an empty or idle system:
P0 = 10
4
10
611
or 40%
(ii) The average number in the system:
Ls = 2
3
4
6
610
6
(iii) The average number in the queue:
Lq = 10
9
2
3x
10
6x
(iv) The average waiting time/unit in the system:
Ws = 4
1
610
11
hour or 15 minutes.
Answer to MTP_Intermediate_Syllabus 2012_Dec2013_Set 1
Directorate of Studies, The Institute of Cost Accountants of India (Statutory Body under an Act of Parliament) Page 4
(b) The project manager’s job is important and challenging. The manager is responsible for
getting work performed but often has no direct, formal authority over most of the people
who perform the job.
The project manager often relies on broader knowledge of the project and skills at
negotiation and persuasion to influence participants. A project manager may have the
assistance of a staff if the project is large. Therefore, it is important that the project
leaders have an effective means of identifying and communicating the planned
activities and the ways in which they are interrelated.
The basic roles for a Project Manager could be broadly grouped under following heads:
(i) Project sing and problem solving. Projectising work as much as possible, e.g., create a
number of projects such as daily, weekly, monthly, quarterly, biannually and annual
package activities of entire plant.
(ii) Defining and maintaining integrity of a project.
(iii) Development of Project Execution Plan. Organization for execution of the plan.
(iv) Setting of cost and time targets for each of the projects, e.g., daily, weekly, monthly
activities, etc
(v) Development of systems and procedures for accomplishment of project objectives
and targets.
(vi) Line up vendors and contractors for the supply of materials and erection skills and
contract Management.
(vii) Negotiation for commitments and Man-management.
(viii) Non-human resource management, including fiscal matters.
(ix) Direction and co-ordination of project activities. Matrix and co-ordinate with other
departments for preparation of drawing, specification, procurement of materials,
providing skills including labour and supervision.
(x) Monitor and control these projects using schedules, budgets and contracts.
(xi) Satisfaction of customer, government and the public. (xii) Achievements of project objectives, cash surplus and higher productivity.
3 (a) A firm produce three products A, B, and C, each of which passes through three
departments: Fabrication, Finishing and Packing. Each unit of Product A requires 3, 4
and 2; each unit of products B requires 5, 4 and 4, while each unit of product C requires
2, 4 and 5 hours respectively in the three departments. Every day, 60 hours are
available in the fabrication department, 72 hours in the finishing department and 100
hours in the packing department. The unit contribution of product A is `5, of product B is `10, and of product C is `8.
Required:
(i) Formulate the problem as an LPP ( Not required to Solve)
(ii) (b) Discuss the Classification of Production Planning and Control Functions (PPC).
[5+7]
Answer of 3:
(a) Let x1, x2 and x3 represent the number of units of products A, B and C respectively. The
given problem can be expressed as a LPP as follows: