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LP PROBLEMS FOR PRACTICE BY GIRISH PHATAK
Q.1 A manufacturing company is engaged in producing three types of
products: A, B and C. The production department produces, each day,
components sufficient to make 50 units of A, 25 units of B and 30 units of
C. The management is confronted with the problem of optimizing the daily
production of products in assembly department where only 100 man – hours
are available daily to assemble the products.
The following additional information is available.
Type of product Profit contribution per
unit of product (Rs)
Assembly time per
product (hrs)
A 12 0.8
B 20 1.7
C 45 2.5
The company has a daily order commitment for 20 units of product A
and a total of 15 units of products B and C. Formulate this problem as an LP
model so as to maximize the total profit.
Q.2 A company has two plants, each of which produces and supplies two
products A and B. The plants can each work up to 16 hours a day. In plant 1,
it takes three hours to prepare and pack 1,000 gallons of A and one hour to
prepare and pack one quintal of B. In plant 2, it takes two hours to prepare
and pack 1,000 gallons of A and 1.5 hours to prepare and pack one quintal
B. In Plant 1 it costs Rs. 15,000 to prepare and pack a thousand gallons of A,
and RS. 28,000 to prepare and pack a quintal of B, whereas these costs are
Rs 18,000 and Rs 26,000, respectively in plant 2. The company is obliged to
produce daily at least 10 thousand gallons of A and 8 quintals of B.
Formulate this problem as an LP model to find out as to how the
company should organize its production so that the required amounts of the
two products be obtained at minimum cost.
Q.3 An electronic company is engaged in the production of two components
C1 and C2 used in radio sets. Each unit of C1 costs the company Rs 5 in
wages and RS 5 in material, while each of C2 costs the company Rs 25 in
wages and RS 15 in material. The company sells both products on one –
period credit terms, but the company’s labour and material expenses must be
paid in cash. The selling price of C1 is Rs 30 per unit and of C2 it is Rs 70
per unit. Because of the strong monopoly of the company for these
components, it is assumed that the company can sell at the prevailing prices
as many units as it produces. The company’s production capacity is,
however, limited by two considerations. First, at the beginning of period ,
the company has an initial balance of Rs 4,000 (cash plus bank credit plus
collections from past credit sales). Second, the company requires production
of each C1 , 2 hours of machine time and 2 hours of assembly time, whereas
the production of each C2 requires 2 hours of machine time and 3 hours of
assembly time. Total machine time available is 2000 hrs whereas total
assembly time available 1400 hrs in the given period. Formulate this
problem as an LP model so as to maximize the total profit to the company.
Q.4 A company has two grades of inspectors 1 and 2, who are to be assigned
for a quality control inspection. It is required that at least 2,000 pieces be
inspected per 8 hour day. Grade 1 inspector can check pieces at the rate of
40 per hour, with an accuracy of 97 per cent. Grade 2 inspector checks at the
rate of 30 pieces per hour with an accuracy of 95 per cent.
The wage rate of a Grade 1 inspector is Rs 5 per hour while that of a
Grade 2 inspector is Rs 4 per hour. An error made by an inspector costs Rs 3
to the company. There are only nine Grade 1 inspectors and eleven Grade 2
inspectors available in the company. The company wishes to assign work to
the available inspectors so as to minimize the total cost of the inspection.
Formulate this problem as an LP model so as to minimize daily inspection
cost.
Q.5 An electronic company produces three types of parts for automatic
washing machines. It purchases casting of the parts from a local foundry and
then finishes the part on drilling, shaping and polishing machines.
The selling prices of parts A, B and C, respectively are Rs 8, Rs 10
and Rs 14. All parts made can be sold. Castings for parts A, B and C,
respectively cost Rs 5, Rs 6 and Rs 10.
The shop possesses only one of each type of machine. Costs per hour
to run each of the three machines are Rs 20 for drilling, Rs 30 for shaping
and RS 30 for polishing. The capacities (parts per hour) for each part on
each machine are shown in the following table :
Machine Capacity per hour
Part A Part B Part C
Drilling 25 40 25
Shaping 25 20 20
Polishing 40 30 40
The management of the shop wants to know how many parts of each
type it should produce per hour in order to maximize profit for an hour’s run.
Formulate this problem as an LP model so as to maximize total profit to the
company.
Q.6 A pharmaceutical company produces two pharmaceutical products. A
and B. Production of both products requires the same process, I and II. The
production of B results also in a by – product C at no extra cost. The product
A can be sold at a profit of Rs 3 per unit and B at a profit of Rs 8 per unit.
Some of this by – product can be sold at a unit profit of Rs 2, the remainder
has to be destroyed and the destruction cost is Re 1 per unit. Forecasts show
that up to 5 units of C can be sold. The company gets 3 units of C for each
unit of B produced. The manufacturing times are 3 hours per unit for A on
process I and II, respectively, and 4 hours and 5 hours per unit for B on
process I and II, respectively. Because the product C results from producing
B, no time is used in producing C. The available times are 18 and 21 hours
of process I and II, respectively. Formulate this problem as an LP model to
determine the quantity of A and B which should be produced, keeping C in
mind, to make the highest profit to the company.
Q.7 A tape recorder company manufacturers models A, B and C which have
profit contributions per unit of Rs 15, Rs 40 and RS 60, respectively. The
weekly minimum production requirements are 25 units for model. A, 130
units for model B and 55 units for model C. Each type of recorder requires a
certain amount of time for the manufacturing of component parts, for
assembling and for packing. Specifically a dozen units of model A require 4
hours for manufacturing, 3 hours for assembling and 1 hour for packaging.
The corresponding figures for a dozen units of model B are 2.5, 4 and 2 and
for a dozen units of model
Q.8 ABC company manufactures three grades of paint Venus, Diana and
Aurora. The plant operates on a three – shift basis and the following data is
available from the production records :
Requirment
of resource
Grade Venus Diana Aurora Availability
(capacity/month)
Special
additive
(kg/litre)
0.30 0.15 0.75 600 tonnes
Milling
(kilolitres per
machine
shift)
2.00 3.00 5.00 100 machine
shifts
Packing
(kiloliters per
shift)
12.00 12.00 12.00 80 shifts
There are no limitations on other resources. The particulars of sales forecasts
and estimated contribution to overheads and profits are given below.
Venus Diana Aurora
Maximum
possible sales per
month (kilolitres)
100 400 600
Contribution
(Rs/kilolitre)
4,000 3,500 2,000
Due to commitments already made, a minimum of 200 kiloliters per
month of Aurora has to be necessarily supplied the next year.
Just as the company was able to finalise the monthly production
programme for the next 12 months, an offer was received from a nearby
competitor for hiring 40 machine shifts per month of milling capacity for
grinding Dianna paint, that could be spared for at least a year. However, due
to additional handling at the competitor’s facility, the contribution from
Dianna will get reduced by Re 1 per litre.
Formulate this problem as an LP model for determining the monthly
production programme to maximise contribution.
Q.9 A garment manufacturer has production line making two styles of shirts. Style 1
require 200 grams of cotton thread, 300 grams of dacron thread, and 300 grams of liner
thread. Style II require 200 grams of cotton thread, 200 grams of dacron thread and 100
gram of liner thread. The manufacturer make the net profit of Rs. 19.50 on Style I ,Rs.
15.90 on Style II. He has in hand inventory of 24kg. Of cotton thread ,26kg of dacron
thread, and 22 kg of liner thread. His immediate problem is to determine the production
schedule given the current inventory to make a maximum profit. Formulate the LPP
Model
Q.10 A firm makes two types of furniture: Chairs and tables. The contribution of each
product as calculated by accounting department is Rs. 20 Per chair and Rs 30 per table.
Both products are processed on three machines M1,M2 and M3.The time required by
each product and total time available per week on each machine are as follow:
Machine Chair Table Available Hours
M1 3 3 36
M2 5 2 50
M3 2 6 60
How should the manufacturer his production in order to maximize contribution?
Q.11 The ABC manufacturing company can make two products p1 and p2.Each of the
product requires time on a cutting machine and a finishing machine. Relevant data are:
P1 P2
Cutting Hours(Per Unit) 2 1
Finishing Hours(Per Unit) 3 3
Profit (Rs. Per unit) 6 4
Maximum Sales(Unit Per
Week)
200
The number of cutting hours available per week is 390 and number of finishing
hours available per week is 810.How much should be produced of each product in order
to achieve the profit for the company?
Q.12 A company make two kinds of leather belts. Belt A is a high quality belt, and belt B
is of low quality. The respective profits are re.0.40 and re.30 per belt. Each belt of type A
requires twice as much time as a belt of type B, and if all belts were of type B, the
company could make 1000 per day. The supply of leather is sufficient for only 800 belts
per day (both A & B combined). But Belt A requires a fancy buckle & only 400 per day
are available. T here are only 700 buckles a day available for belt B.
What should be the daily production of each type of belt? Formulate the LPP.
First Topic Linear Programming Problems for Practice
PROBLEM 1:
XYZ factory manufactures two articles A and B.To manufacture the article A,a certain
machine has to be worked for 1.5 hours and in addition a craftsman has to work for 2
hours.To manufacture the article B, the machine has to be worked for 2.5 hours and in
addition the craftsman has to work for 1.5 hours in a week the factory can avail of 80
hours of machine time and 70 hours of craftsman time.The profit on each article A is
Rs.50 and that on each article B is Rs.40. If all the articles produced can be sold
away,find how many of each kind should be produced to earn the maximum profit per
week.Formulate the problem as LP model.
PROBLEM 2:
An electric company is engaged in the production of two components C1 and C2 used in
T.V. sets. Each unit of C1 costs the company Rs. 25 in wages and Rs. 25 in
material,while each unit of C2 costs the company Rs. 125 in wages and Rs 75 in
material.The company sells both products on one-period credit terms, but the company’s
labour and material expenses must be paid in cash.The selling price of C1 is Rs.150 per
unit and of C2 it is Rs 350 per unit.Because of the strong monopoly of the company for
these components ,it is assumed that the company can sell at the prevailing prices as
many units as it produces. The company’s production capacity is, however, limited by
two considerations. First, at the beginning of period 1, the company has an initial balance
of Rs. 20,000(cash plus bank credit plus collections from past cedit sales). Second , the
company has available in each period 4,000 hours of machine time and 2,800 hours of
assembly time.The production of each C1 requires 6 hours of machine time and 4 hours
of assembly time,whereas the production of each C2 requires 4 hours of machine time
and 6 hours of assembly time.Formulate this problem as an LP model so as to maximize
the total profit of the company.
PROBLEM 3:
IMC manufactures a variety of computing and computer- related equipment.One such
product is a monitor for use with business computer systems and IMC currently has
plans to produce two models of the same monitor: Model A which is the basic ,low-price
monochrome monitor and Model B which is a more sophisticated and expensive colour
graphics monitor.The company is not actually involved in manufacture directly but rather
buys the various component parts which are required for the two models from outside
suppliers.The components are then assembled by IMC to produce Model A and Model B
and each unit produced is then thoroughly inspected for quality and performance.IMC
then sells the two models under its own brand name. There are, therefore, two basic
stages to the production process within the firm- the assembly of the components and the
inspection of the final product. Information about the resources required to produce the
two models has been obtained from the production department and the accounts
department.Model A requires 28 hours of labour to assemble from component parts,while
Model B requires 42 hours.After assembly each computer is then tested in the inspection
department to ensure it is working satisfactorily.Because of the technical complexity of
the product- and the firm’s desire to maintain good quality the control- the inspection
test is time-consuming,with Model A requiring 12 hours of inspection although Model B
requires only 6 hours as more care and time is taken in the assembly stage . At present the
company employs 400 people in the assembly department,each working a 7-hour day;
100 people are presently employed in the inspection department but they work an 8 hour
day.The company presently operates a 6-day working week.Current wage rates are Rs. 20
per hour in assembly and Rs. 15 per hour in inspection.The accounts department has
calculated that in terms of the components and parts, Model A costs Rs.355 and Model B
Rs.565 to produce.Currently the two models sel for Rs. 1,295 and Rs. 1,745
respectively.An additional aspect of the problem ,the firm faces , is that each model
requires a particular component- a microchip that forms part of the monitor’s memory.
The supplier of these chips can provide no more than 600 in any one working week.
FORMULATE a linear programming problem which allows the production manager to
determine how many units of Models A and B should be produced weekly in order to
maximize profits.
PROBLEM 4:
XYZ Electronics company produces three types of parts for automatic washing machine
.It purchases casting of the parts from a local foundry and then furnishes the part of
drilling, shaping and polishing machines.
The selling prices of part A,B and C respectively are Rs.40, Rs.50 and
Rs.70 .All parts made can be sold. Castings for part A,B and C respectively cost Rs.
25,Rs. 30 and Rs.50.
The shop possesses only one of each type of machine. Costs per hour to
run each of the three machines are Rs.100 for drilling,Rs.150 for shaping and Rs. 150 for
polishing. The capacities(parts per hour) for each part on each machine are shown in the
adjoining table:
Machine Capacity per hour
Part A Part B Part C
Drilling 25 40 25
Shaping 25 20 20
Polishing 40 30 40
The management of the shop wants to know how many parts of each
type it should produce per hour in order to maximize profit for an hour’s run. Formulate
the problem as an LP model.
PROBLEM 5:
Ex-servicemen Airport Services Company is considering the purchase of new vehicle for
the transportation between the Delhi airport and hotels in the city.There are three vehicles
under consideration: station wagons, minibuses and large buses.The purchase price would
be Rs. 1,45,000 for each station wagon, Rs. 2,50,000 for the minibus and Rs. 4,00,000 for
the large bus. The Board of Directors has authorized a maximum amount of Rs.
50,00,000 for these purchases. Because the heavy air travel, the new vehicles would be
utilized at maximum capacity regardless of the type of vehicles purchased. The expected
net annual profit would be Rs. 15,000 for the station wagon ,Rs. 35,000 for the minibus
and Rs. 45,000 for the large bus. The company has hired 30 new drivers for the new
vehicles. They are qualified drivers for all three types of vehicles. The maintenance
department has the capacity to handle an additional 80 wagon stations. A minibus is
equivalent of 5/3 wagon stations and each large bus is equivalent to 2 station wagons in
terms of their use of the maintenance department. Determine the optimal number of
vehicles to be purchased in order to maximize profit. FORMULATE the problem as LP
model.
PROBLEM 6:
Vitamins V and W are found in two different foods F1 and F2.One unit of food F1
contains 2 units of vitamin V and 5 units of vitamin W. One unit of food F2 contains 4
units of vitamin V and 2 units of vitamin W. One unit of food F1 and F2 cost Rs. 30 and
25 respectively. The minimum daily requirements(for a person) of vitamin V and W is
40 and 50 units respectively. Assuming that anything in excess of daily minimum daily
requirement of vitamin V and W is not harmful, find out the optimal mixture of food F1
and F2 at the minimum cost which meets the daily minimum requirement of vitamins V
and W. FORMULATE this as a Linear Programming model.
PROBLEM :7
A company is making two products A and B .T he cost of producing one unit of A and B
is Rs 60 and Rs 80 respectively .As per the agreement, the company has to supply at least
200 units of product B to its regular customers. One unit of product A requires one
machine hour whereas product B has machine hours available abundantly within the
company.Total machine hours available for product A are 400 hours. One unit each of
product A and B requires one labour hour each and total of 500 labour hours are
available. The company wants to minimize the cost of production b satisfying the given
requirements. FORMULATE the problem as a linear programming problem.
PROBLEM :8
Frontier bakery has received order from a company M/s Bodhraj Ltd., for the supply of
high protein biscuits. The order will require 1000 Kg. of biscuits mix which is made from
4 ingredients R,S T and U which cost Rs.16,Rs. 4,Rs. 6 and Rs.2per Kg. respectively.
The batch must contain a minimum of 400 Kilos of protein, 250 kilos of fat, 300 kilos of
carbohydrates and 50 Kilos of sugar. The ingredients contain the following percentage by
weight:
Ingredients Protein Fat Carbohydrates Sugar Filler
R
S
T
U
50% 30% 15% 5% 0%
10% 15% 50% 15% 10%
30% 5% 30% 30% 5%
0% 5% 5% 30% 60%
Only 150 kilos of S and 200 kilos of T are immediately available.
Draft a suitable LP model.
PROBLEM :9
A 24-hour supermarket has the following minimal requirements for security officers:
Table 1: STAFFING REQUIREMENTS
TIME OF DAY MINIMUM NUMBER
OF CASHIERS REQUIRED
MIDNIGHT – 4AM 7
4 AM – 8 AM 20
8 AM - NOON 14
NOON – 4PM 20
4 PM – 8 PM 10
8 PM - MIDNGHT 5
TABLE 2: SHIFT SCHEDULE
SHIFT STARTING
TIME
ENDING
TIME
1
2
3
4
5
6
MIDNIGHT
4AM
8AM
NOON
4PM
8PM
8AM
NOON
4PM
8PM
MIDNIGHT
4AM
Shift 1 follows immediately after shift 6. An officer works 8 consecutive hours, starting
at the beginning of one of the six periods. The personnel manager wants to determine
how many officers should work each shift in order to minimize the total number of
officers employed while still satisfying the staffing requirement.
Formulate the problem as a linear programming problem.
PROBLEM :10
A media specialist plans to allocate advertising expenditure in three media whose unit
costs of a message are Rs. 1500; Rs.1250 and Rs.1000 respectively. The total advertising
budget available for the year is Rs. 50000.The first medium is a monthly magazine and it
is desired to advertise not more than once in one issue. At least five advertisements
should appear in the second medium and the no of advertisement in the third medium
should strictly lie between 6 and 10.The effective audience for unit advertisement in the
three media is given below:
Medium: 1 2 3
Expected effective audience: 50,000 40,000 25,000
Formulate a linear programming problem to find the optimal allocation of advertisement
in three media that would maximize the total effective audience.
PROBLEM :11
A person is interested in investing Rs.5,00,000 in a mix of investments. The
investment choices and expected rates of return on each one of them are :-
Investment Projected Rate of Returns
Mutual Fund A 0.12
Mutual Fund B 0.09
Money Market Fund 0.08
Government Bonds 0.085
Share Y 0.16
Share X 0.18
The investor wants at least 35 per cent of his investment in government bonds.
Because of the higher perceived risk of the two shares, he has specified that the combined
investment in these not to exceed Rs.80,000. The investor has also specified that atleast
20 per cent of investment should be in the money market fund and that the amount of
money invested in share should not exceed the amount invested in mutual fund. His final
investment condition is that the amount invested in mutual fund A should be no more
than the amount invested in mutual fund B. the problem is to decide the amount of money
to invest in each alternative so as to obtain the highest annual total return. FORMULATE
the above as linear programming problem.
PROBLEM :12
In a chemical industry two products A and B are made involving two operations. The
production of B also results in a by-product C. the product A can be sold at a profit of Rs.
3 per unit and B at a profit of Rs. 8 per unit. The by-product C has a profit of Rs. 2 per
unit. Forecasts show that upto 5 units of C can be sold. The company gets 3 units of C for
each unit of B produced. The manufacturing times are 3 hrs per unit for A on each of the
operation one and two and 4 hrs and 5 hrs per unit for B on operations one and two
respectively. Because the product C results from producing B, no time is used in
producing C. the available times are 18 hrs and 21 hrs of operation one and two
respectively. The company desires to know that how much A and B should be produced
keeping C in mind to make the highest profit. FORMULATE LP model for this problem.
PROBLEM :13 A public limited company is planning its capital structure that will consist of equity
capital, 15 % debentures and term-loans. Debentures are to be repaid on face value,
interest rate is payable half yearly and annualized cost of issue of debenture is ½ %.
Interest on term-loan is 18% p.a. to be paid annually while the cost of equity is estimated
as 20%. It is decided not to have outsiders funds not more than 2 times of equity fund;
also the amount of term-loan must be at least 50% of the debenture amount.
FORMULATE a suitable LP model so as to minimize average cost of capital of the
company.
PROBLEM.14
A mutual fund has cash resources of Rs. 200 million for investment in diversified
portfolio. Table below shows the opportunities available, their estimated annual yields,
risk factors and term period details.
FORMULATE a suitable LP model to find the optimal portfolio that will maximize
returns, considering the following policy guidelines:
Investment type Annual Yield (%) Risk factors Time period (years)
Bank Deposits 9.5 0.02 6
Treasury notes 8.5 0.01 4
Corporate Deposits 12.0 0.08 3
Blue-chip Stocks 15.0 0.25 5
Speculative Stocks 32.5 0.45 3
Real Estate 35.0 0.40 10
All the funds available may be invested
Weighted average period of at least 5 years as planning horizon.
Weighted average risk factor not to exceed 0.20.
Investment in real estate and speculative stocks to be not more than 25 % of the money
invested in total.
PROBLEM.15 A company has the following independent projects available:
Project cash flows (Rs.’000)
Year A B C D E F
0 (100) - - (40) - (30)
1 (50) (60) - (60) (120) (10)
2 (10) (70) (40) 50 100 20
3 70 10 (80) 10 (10) 10
Cash flows extend beyond year 3 but all are cash inflows for each project
NPV
(Rs.‘000) 20 15 10 30 10 5
New capital for these projects is limited to :
Year 0 Rs. 1,20,000
Year 1 Rs. 2,00,000
Year 2 Nil
Year 3 Nil
Cash generated from these investments can be re-invested in other projects in the same
year.
EXPRESS the above problem in LP format, assuming the objective of the company is to
maximize NPV and the projects are divisible.
PROBLEM :16 A ship has three cargo loads--- Forward, after and center. The capacity limits are :
Weight (tons) Volume (in cubic Ft. )
Forward 2,000 1,00,000
Center 3,000 1,35,000
After 1,500 30,000
The following cargos are offered. The shipowner may accept all or any part of each
commodity.
Commodity Weight (tons) Volume (in cubic Ft. ) Profit per tonne ( Rs.)
A 6,000 60 150
B 4,000 50 200
C 2,000 25 125
In order to preserve the trim of the ship, the weight in each load must be proportional to
the capacity in tones. The cargo is to be distributed so as to maximize the profit.
FORMULATE the problem as LP model.
PROBLEM :17
The PQR stone company sells stones secure from any of the three adjacent quarries. The
stone sold by the company must conform to the following specifications:
Material X equal to 30%
Material Y equal to or less than 40%
Material Z between 30% and 40%
Stone from quarry A costs Rs. 100 per tonne and has the following properties:
Material X – 20%
Material Y – 60%
Material Z – 20%
Stone from quarry B costs Rs. 120 per tonne and has the following properties:
Material X – 40%
Material Y – 30%
Material Z – 30%
Stone from quarry C costs Rs. 150 per tonne and has the following properties:
Material X – 10%
Material Y – 40%
Material Z – 50%
From what quarries should PQR stone company secure rocks in order to minimize cost
per tonne of rocks?
PROBLEM 18
Use Simplex Method to solve the following L.P. Problem
Max.Z = 6x1 + 8x2
Subject to : 30x1 + 20x2 <300
5x1 + 10x2 < 110
x1 + x2 >0
PROBLEM 19
Use simplex method to solve the following L P problem :
Max.Z. = 6 x1 + 8 x2
Subject to Constraints :
2 x1 + 3 x2 < 16
4 x1 + 2 x2 < 16
PROBLEM 20
Use simplex method to solve the following LP Problem
Max Z = 4 x1 + 5x2+8x3
Subject to : X1 + X2 + X3 + < 100
3 x1 + 2x2 + 4x3 < 500
x1, x2, x3, >0
Case 1 Advertising media mix
An advertising co. wishes to plan an advertising campaign in three different media
television , radio , magazine . The purpose of advertising is to reach as many potential
customers as possible . Results of market study are as
given below
T.V. Prime
day
TV prime
time
Radio magazi
ne
Cost of an advertising unit 40000 75000 30000 15000
No of potential customers reached
per unit
400000 900000 500000 200000
No of woman customers reached
per unit
300000 400000 200000 100000
The co. does not want to spend more than Rs.8,00,000 on advertising.it is further require
that
(!) at least 2 million exposures take place among women .
(!!) advertising on television be limited to Rs. 5,00,000
(!!!) at least advertising unit be brought on prime day and two units on prime time;
(!V) the no. of advertising units on radio and magazine should each be between 5 and 10.
Formulate this problem as a lp model to maximise customer reach
Case 2 Advertising media mix
A businessman opening a new restaurant and has budgeted Rs 8,00,000 for advertising in
the coming month.
He is considering 4 types of advertising
(!) 30 seconds television commercial
(!!) 30 seconds radio commercials
(!!!) half page advertisement in news paper
(!V) full page advertisement in a weekly magazine, which will appear 4 times during the
coming month.
The owner wishes to reach families with income both over and under Rs.50000. The
amount of exposure to
families of each type and the cost of the each of the media is shown below
Media Cost of
advertisement
Exposure to families with annual
income over 50000
Exposure to families
with annual income
under50000
Television 40000 200000 300000
Radio 20000 500000 700000
News
paper
15000 300000 150000
Magazine 5000 100000 100000
To have balanced campaign, the owner has determined the following restrictions
(!) no more than 4 TV Ads.
(!!) no more than 60% of all advertisement in news paper and magazine.
(!!!) there must be 30,00,000 exposure to families with income over than 50000
(!!!) there must be 45,00,000 exposure to families with income under than 50000
formulate the LP model to determine the no of each type of advertisement to pursue so as
to maximise the
total no of exposure
Case 3 Advertising agency Campaign
An adv. Agency is preparing an adv. Campaign for a group of agencies. These agencies
have decided that
their target customer should have following characteristics with importance as given
below
Characteristics Weightage
Age 25-40 yr. 20
Annual income Above 60000 30
Female Married 50
The agency has made a careful analysis of three media and has compiled the following
data
Data item Woman’s magazine Radio Television
Age 25-40 yr. 80 % 70 % 60 %
Annual income
above 60000
60 % 50 % 45 %
Females / married 40 % 35 % 25 %
Min. No. of adv.
Allowed
10 5 5
Cost per
advertisement
9500 25000 100000
Max. No. Of Adv.
Allowed
20 10 10
Audience size(1000) 750 1000 1500
The budget for launching the Adv. Campaign is RS 10,00,000 formulate this problem as
a IP model for the
agency to maximise the total no of effective exposure. Case 4
For XYZ Ltd the following data are relevant to its products L and P:
Per unit Product L Rs
Product p Rs
Selling Price 200.00 240.00
Costs: Direct materials 45.00 50.00
Direct wages:
Department 1 16.00 20.00
2 22.50 13.50
3 10.00 30
Variable overhead 6.50 11.50
Fixed overhead is budgeted at Rs 275000 per annum. Relevant data for each department are:
Number of employees
Hours per employee per week
Wage rate per hour (Rs)
Department: 1 20 40 2.00
2 15 40 2.25
3 18 40 2.50
Formulate as LP to maximize contribution
Case 5
a) A firm produces 5 different products from a single raw material. Raw materials
is available in abundance at Rs. 6 per Kg.The labour rate is Rs. 8 per hour for all products. The plant capacity is 21000 labour hours for the budget period. Production facilities can produce all the products. The factory overhead rate is Rs. 8 per hour, comprising Rs. 5.60 per hour as fixed overheads and Rs. 2.40 per hour as variable overheads. The selling commission is 10 percent of the product price. Given the following information, formulate LPP to maximize the Company’s profits.
Product Market demands(units)
Selling price per units(Rs)
Labour hours required per unit
Raw material required per unit (in gms)
A 4000 32.00 1.00 700
B 3600 30.00 0.80 500
C 4500 48.00 1.50 1500
D 6000 36.00 1.10 1300
E 5000 44.00 1.40 1500
B) Assume, in above situation, 3500 hours of overtime working is possible. It will result in additional fixed overheads of Rs 20000 a doubling of labour rates and a 50 percent increase in variable overheads. Formulate LPP to decide about the overtime working. Case 6
A manufacturer of biscuits is considering four types of gift packs containing
three types of biscuits. Orange cream (OC), Chocolate cream (CC) and
Wafers (W). A market research study conducted recently to assess the
preference of the consumers shows the following types of assortments to be
in good demand :
Assortments Contents Selling price per Kg (Rs)
A Not less than 40% of OC 20
Not more than 20% of CC
B Not less than 20% of OC 25
Not more than 40% of CC
Any quantity of W
C Not less than 50% of OC 22
Not more than 10% of CC
Any quantity of W
D No restrictions 12
For the basics, the manufacturing capacity and costs are given below :
Type of biscuit Plant capacity (kg/day) Manufacturing cost
(Rs/kg)
OC 200 8
CC 200 9
W 150 7
Formulate this problem as an LP model to find the production
schedule which maximizes the profit, assuming that there are no market
restrictions.
