Solapur University Question Paper
M.C.A. (Part – II) (Semester – IV) Examination, 2014
(Commerce and Management Faculty)
OPTIMIZATION TECHNIQUES
Day and Date : Monday, 12-5-2014 Total Marks : 70
Time : 3.00 p.m. to 6.00 p.m.
Instructions : 1) Q. 1 and Q. 7 are compulsory.
2) Attempt any two questions from Q. 2 to Q. 4.
3) Attempt any one questions from Q. 5 to Q. 6.
4) All questions carry equal marks.
1. A) Select correct alternatives : 7
1) LP theory states that the optimal solution to any problem will lie at
a) the origin
b) a corner point of the feasible region
c) the highest point of the feasible region
d) the lowest point in the feasible region
2) Consider the following linear programming problem
Maximize 5X + 6Y
Subject to : 4X + 2Y < 420
1X + 2Y < 120, all variables > 0
Which of the following points (X, Y) is feasible ?
a) (50, 40) b) (30, 50)
c) (60, 30) d) (90, 20)
P.T.O.
Seat
No.
SLR-GL – 29 -2-
3) In converting a less-than-or-equal constraint for use in a simplex table, we
must add
a) a surplus variables
b) a slack variable
c) an artificial variable
d) both a surplus and a slack variable
4) Which of the following is not a type of integer programming problem ?
a) pure integer programming problem
b) blending problem
c) zero-one programming problem
d) mixed-integer programming problem
5) Time an activity would take assuming very unfavorable conditions is
represented by the
a) optimistic time (a)
b) most likely time (m)
c) deterministic time (d)
d) pessimistic time (b)
6) In the A/B/C designation for queuing systems, the B term represents
information about
a) arrival rates
b) service times
c) number of channels
d) size of the queue
7) The main purpose of inventory management is usually to
a) minimize the cost of purchasing inventory
b) maximize customer satisfaction
c) increase the safety stock level
d) minimize the overall cost of inventory
-3- SLR-GL – 29
B) State true or false : 7
1) If the right-hand side of a constraint is changed, the feasible region will not
be affected and will remain the same.
2) The situation that occurs when we have no solution that satisfies the
constraints is referred to as infeasibility.
3) All variables in a linear programming problem (real, slack, surplus, or
artificial) must be positive.
4) The transportation problem is a good example of a pure integer programming
problem.
5) In PERT, we assume that activity times are deterministic, while in CPM
we assume that activity times are probabilistic.
6) In the multichannel model (M/M/m) we must assume that the average
service time for all channels is the same.
7) ABC Analysis divides inventory into three groups.
2. a) Solve the following LPP by using 2-phase Simplex method 7
Minimizes Z = x1 + x2
Subject to : 2x1 + 4x2
> 4
x1 + 7x2
> 12
and x1, x2
> 0 and integers.
b) Solve the following assignment problem : 7
A company has one surplus truck in each of the cities A, B, C, D and E and
one deficient truck in each of the cities 1, 2, 3, 4, 5 and 6. The distance
between the cities (in Km) is shown in matrix below
From City
Surplus
To City (deficit)
123456
A 12 10 15 22 18 8
B 10 18 25 15 16 12
C 11 10 3 8 5 9
D 6 14 10 13 13 12
E 8 12 11 7 13 10
Find the assignment of truck from cities in surplus to cities in deficit so that
the total distance covered by vehicles in minimum.
3. a) A steel company has three open hearth furnaces and five rolling mills.
Transportation costs (Rs./quintal) for shipping steel from furnaces to rolling
mills are shown in the following table 7
M1 M2 M3 M4 M5 Supply
F1 42326 8
F2 5 4 5 2 1 12
F3 6 5 4 7 7 14
Demand 44688
What is the optimal shipping schedule ?
SLR-GL – 29 -4-
b) Solve the following integer programming problem using branch and bound
method 7
Minimizes Z = 3x1 + 2.5x2
Subject to : x1 + 2x2
> 20
3x1 + 2x2 > 50
x1, x2 > 0 and integers.
4. a) Explain the following term in LPP 7
i) Feasible solution
ii) Optimum solution
iii) Slack variable
iv) Objective function
v) Constraints.
b) A Xerox machine in an office is operated by a person who does other jobs
also. The average service time for a job is 6 minutes per customers. On
averages, every 12 minutes one customers arrive for Xeroxing. Find.
a) the Xerox machine utilization,
b) percentage of times that an arrival has not to wait,
c) average time spent by a customer,
d) average queue length
e) the arrival rate, if the management is willing to deploy the person exclusive
for Xeroxing when the average time spent by a customer exceeds
15 minutes. 7
5. a) Explain the following term : 7
i) Optimistic Time
ii) Pessimistic Time
iii) Most likely time regarding an activity
iv) PERT.
-5- SLR-GL – 29
b) The research department of Hindustan Lever has recommended the marketing
department to launch the shampoo of three different types. The marketing
manager has to decide one of the types of shampoo to be launched under the
following estimated pay-off for various levels of sales. 7
Types of Shampoo
Estimated Levels of Sales (Units)
Rs. 15,000 Rs. 10,000 Rs. 5,000
Egg Shampoo 30 10 10
Clinic Shampoo 40 15 5
Delux Shampoo 55 20 3
What will be the marketing manager’s decision ?
i) Maximin
ii) Minimax
iii) Maximax
iv) Laplace.
6. a) Explain the inventory model with shortage. 7
b) Consider the following data : 7
Unit cost : Rs. 100
Order Cost : Rs. 160
Inventory carrying cost : Rs. 20
Back-order cost (due to stockout cost) : Rs. 10
Annual demand : 1000 units
Compute the following :
a) Minimum cost order quantity
b) Time between orders
c) Maximum number of back orders
d) Maximum inventory level
e) Overall annual cost.
SLR-GL – 29 -6-
7. a) What are the types of decision making environment ? Explain any one in
details. 7
b) The time estimates (in weeks) for the activities of a PERT network are given
below : 7
Activity
Sequence
Time Duration
Optimistic Most Likely Pessimistic
1 − 2 11 7
1 − 3 14 7
1 − 4 22 8
2 − 5 11 1
3 − 5 2 5 14
4 − 6 25 8
5 − 6 3 6 15
i) Draw the project network and identify all the path through it.
ii) Determine the expected project length.
iii) Calculate standard deviation and variance of the project length.
M.C.A. (Part – II) (Semester – IV) Examination, 2014
(Commerce and Management Faculty)
OPTIMIZATION TECHNIQUES
Day and Date : Monday, 12-5-2014 Total Marks : 70
Time : 3.00 p.m. to 6.00 p.m.
Instructions : 1) Q. 1 and Q. 7 are compulsory.
2) Attempt any two questions from Q. 2 to Q. 4.
3) Attempt any one questions from Q. 5 to Q. 6.
4) All questions carry equal marks.
1. A) Select correct alternatives : 7
1) LP theory states that the optimal solution to any problem will lie at
a) the origin
b) a corner point of the feasible region
c) the highest point of the feasible region
d) the lowest point in the feasible region
2) Consider the following linear programming problem
Maximize 5X + 6Y
Subject to : 4X + 2Y < 420
1X + 2Y < 120, all variables > 0
Which of the following points (X, Y) is feasible ?
a) (50, 40) b) (30, 50)
c) (60, 30) d) (90, 20)
P.T.O.
Seat
No.
SLR-GL – 29 -2-
3) In converting a less-than-or-equal constraint for use in a simplex table, we
must add
a) a surplus variables
b) a slack variable
c) an artificial variable
d) both a surplus and a slack variable
4) Which of the following is not a type of integer programming problem ?
a) pure integer programming problem
b) blending problem
c) zero-one programming problem
d) mixed-integer programming problem
5) Time an activity would take assuming very unfavorable conditions is
represented by the
a) optimistic time (a)
b) most likely time (m)
c) deterministic time (d)
d) pessimistic time (b)
6) In the A/B/C designation for queuing systems, the B term represents
information about
a) arrival rates
b) service times
c) number of channels
d) size of the queue
7) The main purpose of inventory management is usually to
a) minimize the cost of purchasing inventory
b) maximize customer satisfaction
c) increase the safety stock level
d) minimize the overall cost of inventory
-3- SLR-GL – 29
B) State true or false : 7
1) If the right-hand side of a constraint is changed, the feasible region will not
be affected and will remain the same.
2) The situation that occurs when we have no solution that satisfies the
constraints is referred to as infeasibility.
3) All variables in a linear programming problem (real, slack, surplus, or
artificial) must be positive.
4) The transportation problem is a good example of a pure integer programming
problem.
5) In PERT, we assume that activity times are deterministic, while in CPM
we assume that activity times are probabilistic.
6) In the multichannel model (M/M/m) we must assume that the average
service time for all channels is the same.
7) ABC Analysis divides inventory into three groups.
2. a) Solve the following LPP by using 2-phase Simplex method 7
Minimizes Z = x1 + x2
Subject to : 2x1 + 4x2
> 4
x1 + 7x2
> 12
and x1, x2
> 0 and integers.
b) Solve the following assignment problem : 7
A company has one surplus truck in each of the cities A, B, C, D and E and
one deficient truck in each of the cities 1, 2, 3, 4, 5 and 6. The distance
between the cities (in Km) is shown in matrix below
From City
Surplus
To City (deficit)
123456
A 12 10 15 22 18 8
B 10 18 25 15 16 12
C 11 10 3 8 5 9
D 6 14 10 13 13 12
E 8 12 11 7 13 10
Find the assignment of truck from cities in surplus to cities in deficit so that
the total distance covered by vehicles in minimum.
3. a) A steel company has three open hearth furnaces and five rolling mills.
Transportation costs (Rs./quintal) for shipping steel from furnaces to rolling
mills are shown in the following table 7
M1 M2 M3 M4 M5 Supply
F1 42326 8
F2 5 4 5 2 1 12
F3 6 5 4 7 7 14
Demand 44688
What is the optimal shipping schedule ?
SLR-GL – 29 -4-
b) Solve the following integer programming problem using branch and bound
method 7
Minimizes Z = 3x1 + 2.5x2
Subject to : x1 + 2x2
> 20
3x1 + 2x2 > 50
x1, x2 > 0 and integers.
4. a) Explain the following term in LPP 7
i) Feasible solution
ii) Optimum solution
iii) Slack variable
iv) Objective function
v) Constraints.
b) A Xerox machine in an office is operated by a person who does other jobs
also. The average service time for a job is 6 minutes per customers. On
averages, every 12 minutes one customers arrive for Xeroxing. Find.
a) the Xerox machine utilization,
b) percentage of times that an arrival has not to wait,
c) average time spent by a customer,
d) average queue length
e) the arrival rate, if the management is willing to deploy the person exclusive
for Xeroxing when the average time spent by a customer exceeds
15 minutes. 7
5. a) Explain the following term : 7
i) Optimistic Time
ii) Pessimistic Time
iii) Most likely time regarding an activity
iv) PERT.
-5- SLR-GL – 29
b) The research department of Hindustan Lever has recommended the marketing
department to launch the shampoo of three different types. The marketing
manager has to decide one of the types of shampoo to be launched under the
following estimated pay-off for various levels of sales. 7
Types of Shampoo
Estimated Levels of Sales (Units)
Rs. 15,000 Rs. 10,000 Rs. 5,000
Egg Shampoo 30 10 10
Clinic Shampoo 40 15 5
Delux Shampoo 55 20 3
What will be the marketing manager’s decision ?
i) Maximin
ii) Minimax
iii) Maximax
iv) Laplace.
6. a) Explain the inventory model with shortage. 7
b) Consider the following data : 7
Unit cost : Rs. 100
Order Cost : Rs. 160
Inventory carrying cost : Rs. 20
Back-order cost (due to stockout cost) : Rs. 10
Annual demand : 1000 units
Compute the following :
a) Minimum cost order quantity
b) Time between orders
c) Maximum number of back orders
d) Maximum inventory level
e) Overall annual cost.
SLR-GL – 29 -6-
7. a) What are the types of decision making environment ? Explain any one in
details. 7
b) The time estimates (in weeks) for the activities of a PERT network are given
below : 7
Activity
Sequence
Time Duration
Optimistic Most Likely Pessimistic
1 − 2 11 7
1 − 3 14 7
1 − 4 22 8
2 − 5 11 1
3 − 5 2 5 14
4 − 6 25 8
5 − 6 3 6 15
i) Draw the project network and identify all the path through it.
ii) Determine the expected project length.
iii) Calculate standard deviation and variance of the project length.
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