Ask Question, Ask an Expert


Ask Operation Research Expert

Q.1  A company makes two products X and Y. Mr. Girish, Production Manager has estimated a unit profit of Rs. 124 and Rs. 80 on these products X and Y respectively. Both the products pass through two departments for processing and the times in minutes per unit taken by X and Y are

                         Product X    Product Y
Department 1        150             90
Department 2        100            120

Currently the production manager is provided with 225 hours per week in department 1 and 200 hours in department 2. The company is selling its products to countries of EEC, and can sell all it can produce of X, but the EEC quotas restrict the sale of Y to a maximum of 75 units per week.
The production manager currently is manufacturing and selling 30 units of X and 75 units of Y per week.
The company wishes to maximize contribution margin and therefore has directed Mr. Girish to review his production plan. Mr. Girish is considering several possibilities including.

i.    altering the production plan if it could be proved that there is a better plan than the current one.

ii.    Increasing the availability of hours for either department 1 or department 2. The extra costs involved in increasing the capacity are Re. 0.5 per hour for each department.

iii.    Transfer some of their allowed sales quota for product Y to another company. Because of the commitment, the company could always retain a minimum sales level of 30 units.

You are required to help Mr. Girish in the following

i.    find out the optimum production plan using the existing capacities and state the extra contribution that would be achieved compared with the existing plan.

ii.    Advise Mr. Girish whether the company should increase the capacity of either department 1 or department 2 and, if so, by how many hours and what the resulting increase should in contribution would be over that, find outd in the improved production plan.

iii.    find out the minimum price per unit for which the company could sell the rights to their sales quota, down to the minimum level, given the plan in

(a) as a starting point.

Q. 2     A cement company has three factories A, B & C which manufacture cement which is then transported to four distribution centers. The quantity of monthly production of each factory, the demand of each distribution center and the associated transportation cost per quintal are given below.

Factory                 Distribution center                Monthly production
                             W     X        Y         Z   
A                           10    8        5         4                        7,000
B                            7     9       15         8                        8,000
C                            6    10       14        8                      10,000
Monthly demand    6,000    6,000    8,000    5,000   

(a)    Suggest the optimal transportation schedule

(b)    Is there any other transportation schedule which is equally attractive? If so prepare that.

(c)    If the company wants at least 5000 quintals of cement to be transported from factory C to distribution center Y, will the transportation schedule be any different? If so, then what is the new optimal schedule and the effect on the cost?

(d)    Suppose the company desires to send at most 500 quintals of cement from factory C to distribution center Y, what will the new optimal schedule be? Also obtain the transportation cost in this case.

Q.3 A firm uses three machines in the manufacture of three products. Each unit of product A requires 3 hours on machine I, 2 hours on machine II and 1 hour on machine III. Each unit of product B requires 4 hours on machine I, 1 hour on machine II and 3 hours on machine III. While unit of product C requires 2 hours on each of the three machines. The contribution of each product is Rs.30, Rs. 40 and Rs 35 respectively. The machine hours available on the three machines are 90, 54 & 93 respectively.
Formulate the above as LPP

1. Obtain the optimal solution by simplex method. Which of these three products are manufactured by the firm?

2. find out the percentage of capacity utilization in optimal solution

3. What are the shadow prices of machine hours?

4. Is the optimal solution degenerate?

Q.4 A small garment –making unit has five tailors stitching five different types of garments. All the five tailors are capable of stitching all the five types of garments. The output per tailor and the profit in rupees for each type of garment are given below


Tailors                1        2        3        4        5
   A                     7        9        4        8        6
   B                    4        9        5        7        8
   C                    8        5        7        9        8
   D                   6        5        8       10      10
   E                    7        8      10         9        9

Profit (Rs)        2        3        2        3        4
Per garment       

i.  Which type of garment should be assigned to which tailor in order to maximize profit assuming that there are no other constraints?

ii. If tailor D is not available during the specific period and no other substitute tailor is available, what should be the optimal assignment?

Q.5 The following table shows all the necessary information on the availability of supply to each warehouse, the requirement of each market and unit transportation cost from each warehouse to each market.

                 P    Q     R    S    Supply
A               6    3      5    4       22
B               5    9      2    7       15
C               5    7      8    6        8
Demand    7    12    17   9

The shipping clerk has worked out the following schedule from experience: 12 units from A to Q, 1 unit from A to R, 9 units from A to S, 15 units from B to R, 7 units from C to P, and 1 unit from C to R. Check whether the clerk has optimal schedule.

Q.6 The following table gives details of a project

                    Normal            Crash
Activity    Predecessor       Time    Cost(Rs’000)    Time         Cost(Rs’000)
     A                -                   10           20                  7             30
     B                -                    8            15                   6            20
     C                B                   5             8                   4            14
     D                B                   6            11                  4            15   
     E                B                   8             9                   5            15
     F                 E                   5             5                  4              8
     G             A, D, C             12            3                  8              4

Indirect cost is Rs. 400 per day. Find the optimal duration and the associated project cost

Operation Research, Management Studies

  • Category:- Operation Research
  • Reference No.:- M91541

Have any Question? 

Related Questions in Operation Research

For 100 consecutive days a company making nutritional

For 100 consecutive days, a company making nutritional supplements has measured the amount of a protein the company puts into its protein bars. Each day, the company takes a sample of 6 protein bars. The average across a ...

Business models and consumer choices please respond to the

"Business Models and Consumer Choices" Please respond to the following: Debate It: Take a position on the following statement: Copyright laws protect rights of creative independent artists against a large corrupt music i ...

In every organization inputs of some kind services

In every organization, inputs of some kind (services, information, and/or products) are transformed into outputs (services, information, and/or products) on an ongoing, continuous basis, which are of value to internal or ...

Consider you need to conduct a business forecastdescribe

Consider you need to conduct a business forecast. Describe your forecast process according to the following steps: - Define the purpose of the forecast o Establish a time horizon - Select a forecasting technique o Gather ...

Read and answer following questions with1-2 pages papermike

"Read and answer following questions with1-2 pages paper." Mike graduated from school a few months ago. He applied to various companies and has decided to take a position as a supervisor at a well-known local restaurant. ...

Short essays no required length1 discuss how occupational

Short essays (no required length) 1. Discuss how occupational safety and health laws and regulations are established, implemented and possibly altered. 2. Compare and contrast this with the establishment of environmental ...

Directions the assignment focuses on your own understanding

DIRECTIONS The assignment focuses on your own understanding of the team's group project. Early in the conceptual phase of a new product, team members should begin to think about all of the things that need to be done to ...

A 75-year-old female is an inpatient in bed 1 of room 10 on

A 75-year-old female is an inpatient in bed #1 of Room 10 on a medical telemetry unit. She has been admitted for pneumonia. She is slightly confused. No family is with her in the hospital at this time. The nurse introduc ...

Questionusing minitab andor a cause-and-effect diagram

Question: Using Minitab and/or a cause-and-effect diagram, identify the root cause of the problem you are trying to solve for the process you chose in 1-3. Also, construct a main effects plot, if applicable.

Question 1at the beginning of each day a patient in a

Question 1: At the beginning of each day, a patient in a hospital is classified into one of three conditions; good, fair, or critical. At the beginning of the next day, the patient will either continue to be in the hospi ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

Section onea in an atwood machine suppose two objects of

SECTION ONE (a) In an Atwood Machine, suppose two objects of unequal mass are hung vertically over a frictionless

Part 1you work in hr for a company that operates a factory

Part 1: You work in HR for a company that operates a factory manufacturing fiberglass. There are several hundred empl

Details on advanced accounting paperthis paper is intended

DETAILS ON ADVANCED ACCOUNTING PAPER This paper is intended for students to apply the theoretical knowledge around ac

Create a provider database and related reports and queries

Create a provider database and related reports and queries to capture contact information for potential PC component pro

Describe what you learned about the impact of economic

Describe what you learned about the impact of economic, social, and demographic trends affecting the US labor environmen