HSC Commerce (English Medium) 12th Standard Board Exam - Maharashtra State Board Important Questions for Mathematics and Statistics

Determine `l_92 and l_93, "given that"  l_91 = 97, d_91 = 38 and q_92 = 27/59`

Solve the following minimal assignment problem and hence find minimum time where  '- ' indicates that job cannot be assigned to the machine : 

Solve the following maximal assignment problem :

A departmental head has three jobs and four subordinates. The subordinates differ in their capabilities and the jobs differ in their work
contents. With the help of the performance matrix given below, find out which of the four subordinates should be assigned which jobs ?

In a factory there are six jobs to be performed each of which should go through two machines A and B in the order A - B. The processing timing (in hours) for the jobs arc given here. You are required to determine the sequence for performing the jobs that would minimize the total elapsed time T. What is the value of T? Also find the idle time for machines · A and B.

Five wagons are available at stations 1, 2, 3, 4, and 5. These are required at 5 stations I, II, III, IV, and V. The mileage between various stations are given in the table below. How should the wagons be transported so as to minimize the mileage covered?

In the modification of a plant layout of a factory four new machines M₁, M₂, M₃ and M₄ are to be installed in a machine shop. There are five vacant places A, B, C, D and E available. Because of limited space, machine M₂ cannot be placed at C and M₃ cannot be placed at A. The cost of locating a machine at a place (in hundred rupees) is as follows.

Find the optimal assignment schedule.

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 elapsed time and idle time for each machine.

Find the optimal sequence that minimizes total time required to complete the following jobs in the order ABC. The processing times are given in hours.

If jobs A to D have processing times as 5, 6, 8, 4 on first machine and 4, 7, 9, 10 on second machine then the optimal sequence is ______.

If there are n jobs and m machines, then there will be_______ sequences of doing the jobs.

To use the Hungarian method, a profit maximization assignment problem requires ______.

Choose the correct alternative :

The assignment problem is said to be balanced if it is a ______.

The objective of an assignment problem is to assign ______. 

The time interval between starting the first job and completing the last job including the idle time (if any) in a particular order by the given set of machines is called _______.

The time required for printing of four books A, B, C and D is 5, 8, 10 and 7 hours while its data entry requires 7, 4, 3 and 6 hrs respectively. The sequence that minimizes total elapsed time is ______.

Solve the following problem :

Five jobs must pass through a lathe and a surface grinder, in that order. The processing times in hours are shown below. Determine the optimal sequence of the jobs. Also find the idle time of each machine.

Solve the following problem :

Find the sequence that minimizes the total elapsed time to complete the following jobs. Each job is processed in order AB.

Determine the sequence for the jobs so as to minimize the processing time. Find the total elapsed time and the idle times for both the machines.

Choose the correct alternative:

If there are 3 machines A, B and C, conditions for reducing a 3 machine problem to a 2 machine problem with respect to minimum processing time is ______

If there are n jobs and m machines, then there will be _______ sequence of doing jobs.