Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2

   

Balbharati Maharashtra State Board 12th Commerce Maths Solution Book Pdf Chapter 7 Assignment Problem and Sequencing Ex 7.2 Questions and Answers.

Maharashtra State Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2

Question 1.
A machine operator has to perform two operations, turning and threading on 6 different jobs. The time required to perform these operations (in minutes) for each job is known. Determine the order in which the jobs should be processed in order to minimize the total time required to complete all the jobs. Also, find the total processing time and idle times for turning and threading operations.
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q1
Solution:
Let turning to be A and threading be B.
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q1.1
∴ Observe Min{A, B} = 1 for job 6 on B.
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q1.2
Then the problem reduces to
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q1.3
∴ Now Min {A, B} = 2 for job 4 on A
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q1.4
Then the problem reduce to
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q1.5
Now Min {A, B} = 3 for job 1 on A and job 5 on B
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q1.6
Then the problem reduces to
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q1.7
Now Min {A, B) = 5 for job 3 on A
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q1.8
Only job 2 is left so the optimal sequence is
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q1.9
Worktable is given by
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q1.10
Total elapsed time = 43 minutes
Idle time for A (turning) = 43 – 42 = 1 min
Idle time for B (threshing) = 2 + 4 = 6 min

Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2

Question 2.
A company has three jobs on hand, Each of these must be processed through two departments, in the AB where
Department A: Press shop and
Department B: Finishing
The table below gives the number of days required by each job each department
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q2
Find the sequence in which the three jobs should be processed so as to take minimum time to finish all the three jobs. Also find idle time for both the departments.
Solution:
Observe Min {A, B} = 3 for job II on B.
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q2.1
Then the problem is reduced to
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q2.2
Now Min {A, B} = 4 for job III at B
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q2.3
Now only job I in left
∴ the optimal sequence is given by
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q2.4
The work table is
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q2.5
Total elapsed time = 23 days
Idle time for A = 23 – 19 = 4 days
Idle time for B = 8 days

Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2

Question 3.
An insurance company receives three types of policy application bundles daily from its head office for data entry and filing. The time (in minutes) required for each type for these two operations is given in the following table:
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q3
Find the sequence that minimizes the total time required to complete the entire task. Also, find the total elapsed time and idle times for each operation.
Solution:
Let Data entry be A and filing be B. So
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q3.1
Observe min {A, B} = 90 for policy 1 at A
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q3.2
Then the problem reduces to
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q3.3
Observe min {A, B} = 100 for policy 3 at B
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q3.4
Now only policy 2 is left
∴ The optimal sequence is
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q3.5
Worktable
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q3.6
So Total elapsed time = 490 min
Idle time for A (data entry) = 490 – 390 = 100 min
Idle time for B (filing) = 140 min.

Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2

Question 4.
There are five jobs, each of which must go through two machines in the order XY. Processing times (in hours) are given below. Determine the sequence for the jobs that will minimize the total elapsed time. Also, find the total elapse time and idle time for each machine.
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q4
Solution:
Observe min {x, y} = 2 for job B on x
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q4.1
The problem reduces to
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q4.2
Now min [x, y] = 4 for job A on x
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q4.3
The problem reduces to
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q4.4
Now min [x, y] = 6 for job D on x
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q4.5
The problem reduces to
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q4.7
Now min [x, y] = 8 for job E on y
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q4.6
Now only job C in left
∴ The optimal sequence is
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q4.8
Worktable
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q4.9
Total elapsed time = 60 hrs
Idle time for X = 60 – 56 = 4 hrs
Idle time for Y = 6 hrs

Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2

Question 5.
Find the sequence that minimizes the total elapsed time to complete the following jobs in the order AB. Find the total elapsed time and idle times for both machines.
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q5
Solution:
Observe min {A, B} = 5 for job VI for B and job VII for A
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q5.1
The problem reduces to
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q5.2
Now min {A, B] = 7 for job I on A
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q5.3
The problem reduces to
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q5.4
Now min {A, B] = 10 for job IV on A and B so we have two options.
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q5.5
Or
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q5.6
we take the 1st one.
The problem reduces to
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q5.7
Now min {A, B} = 14 for job V on A and job II and III for job B.
∴ We have
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q5.8
Or
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q5.9
We take the optimal sequence as.
VII – I – IV – V – III – II – VI
Worktable
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q5.10
Total elapsed time = 91 units
Idle time for A = 91 – 86 = 5 units
Idle time for B = 13 units

Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2

Question 6.
Find the optimal sequence that minimizes the total time required to complete the following jobs in the order ABC. The processing times are given in hrs.
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q6
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q6.1
Solution:
(i) Min A = 5, Max B = 5
As min A ≥ max B.
The problem can be converted into two machine problems.
Let G and H be two fictitious machines such that G = A + B and H = B + C we get
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q6.2
Now min {G, H} = 7 for job III & V for G and job I for H
∴ We have two options
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q6.3
Or
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q6.4
We take the first one
The problem reduces to
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q6.5
Min {G, H} = 9 for job IV on H
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q6.6
The problem reduces to
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q6.7
Now min {G, H} = 10 for job II for G and job VII for H
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q6.8
Now job VI is left
∴ The optimal sequence is
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q6.9
The work table is
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q6.10
Total elapsed time = 61 hrs
Idle time for A = 61 – 54 = 7 hrs
Idle time for B = 35 + [61 – 58] = 38 hrs
Idle time for C = 15 hrs

Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2

(ii) Min A = 5, Max B = 5
Min A ≥ Max B.
The problem can be converted into two machine problems.
Let G and H be two fictitious machines such that G = A + B and H = B + C we get
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q6.11
Now min {G, H} = 5 for job 1 for H.
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q6.12
The problem reduces to
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q6.13
Now min {G, H} = 8 for job 2 for G and job H also job 5 for G
∴ We have two options
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q6.14
Or
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q6.15
We take the first one
The problem reduces to
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q6.16
Now min {G, H} = 9 for job 3 for H
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q6.17
Now only job 4 is left
∴ The optimal sequence is
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q6.18
Worktable
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q6.20
Total elapsed time = 40 hrs
Idle time for A = 40 – 32 = 8 hrs
Idle time for B = 19 + [40 – 34] = 25 hrs
Idle time for C = 12 hrs

Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2

Question 7.
A publisher produces 5 books on Mathematics. The books have to go through composing, printing, and binding was done by 3 machines P, Q, E. The time schedule for the entire task in the proper unit is as follows.
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q7
Determine the optimum time required to finish the entire task.
Solution:
Min R = 6, Max Q = 6
As min R ≥ max Q.
The problem can be converted into a two-machine problem.
Let G and H be two fictitious machines such that G = P + Q and H = Q + R we get
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q7.1
Min {G, H} = 9 for books A, D, E for G.
∴ We have more than one option we take
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q7.2
The problem reduces to
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q7.3
Min {G, H} = 8 for book C on H
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q7.4
Now only B is left. So the optimal sequence is
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q7.5
Worktable
Maharashtra Board 12th Commerce Maths Solutions Chapter 7 Assignment Problem and Sequencing Ex 7.2 Q7.6
Total elapsed time = 51 units
Idle time for P = 51 – 32 = 19 units
Idle time for Q = 14 + [51 – 34] = 31 units
Idle time for R = 9 units

Leave a Comment