PROBLEMS FROM UNIVERSITY PAPERS
ON GRAPHICAL / SIMPLEX METHOD
- April 2002
Agashe & co. Plans to reach target audiences belonging to two different monthly income groups, the first with the income group greater than Rs.15000 and second with income less than 15000. The total budget is Rs.200000. For advertising on TV it costs Rs.50000 for one programme whereas advertising on radio cost Rs.20000 per programme. For contract reason at least 3 programmes must be given on TV and number of programmes on radio are limited to 5 only. One TV programme covers 450000 audiences belonging to income group having more than 15000 monthly income & it reaches to 50000 audiences having income less than 15000.similarly. One radio programme reaches to 20000 & 80000 audiences belonging to income above 15000 & below 15000 respectively. Determine the media mix so as to maximize total number of target audience
- April 2002
M/s. Raj & Bilimoria associate produce three items X,Y and Z each of which has to be process through 3 machines P,Q & R Each unit of product X requires 3, 4 & 2 hours on P, Q & R respectively. Similarly each unit of product Y requires 5, 4 & 4 hours on machines P, Q. and R respectively. For product Z the requirements are 2, 4 & 5 hours on the machines P, Q and R respectively. Everyday 60 hours are available on machine P, 72 hours on machine Q & 100 hours on machine R. The unit contribution of these products X, Y and Z is Rs.5, Rs.10 & Rs.8 respectively. Determine the product mix to optimize the objective of the company.
- Oct 2002
SMS company produces three products P,Q and R. all these products have to pass through three machines,m1,m2 and m3.the time required to process each unit of products on each machine and the available capacity of the machines are as follows
Product Time Required Per Unit in minutes
M1 M2 M3
P 4 3 2
Q 4 4 1
R 4 3 2
Available capacity 1200 900 400
In minutes
The profit per unit to be realized from manufacture of products is Rs.20,Rs.12 And Rs.8 respectively. Determine the product mix to maximize the profitability.
- Oct 2002
Mr.X wants to invest an amount unto Rs.30000 in fixed income securities. His financial advisor recommends investing in two bonds P and Q. Bond P yields 7 % andQ yields 10 %. After some considerations he decided to invest at most Rs.12000 in bond Q and at least Rs.6000 in bond P. He also wants the amount invested in bond P to be at least equal to the amount invested in bond Q. What should the financial advisor recommend ifMr.X has to maximize his returns from the investment?
- April 2003
A television manufacturing firm is planning to produce television sets of various designs &specifications. The market research survey indicates that all the three types –flat screen, black screen and normal TV sets will be sold whichever is produced. The firm plans to test the market response first by manufacturing only 200 sets of all the three types all of which will be sold. The firm wants to decide how many of flat screen and black screen TV sets should be produced whereas the numbers of normal type is automatically decided on the basis of first two types. The following table summarizes the estimated prices for all the three types of sets and corresponding expenses for the firm. The firm has hired plant to manufacture these TV sets at fixed charges of rs.200000 for a period of 1 month.
Types Of TV Prices Tube Cost Labour / Material Cost
Flat Screen 10000 3000 4750
Black Screen 7000 2200 2500
Normal 6500 1900 2200
In planning the production following considerations must be taken into account
The marketing management requires at least 120 TV sets to be of flat and black screen type.
At least 35 % but not more than 70 % must be of black screen
At least 10 % of TV sets must be of flat screen
At least 30 % of total sets must be of normal type
The maximum number of flat screen TV sets that can be manufactured at the plant is restricted to 60 only.
The firm wishes to determine the number of TV sets to produce of each type so as to maximize the profit.
- Oct 2003
United fabricators makes two types of auto parts A and B. it buys castings that are to be machined, bored and polished. The capacity of boring is 28 per hour for A and 35 per hour for B and the capacity of polishing is 35 per hour for A and 25 per hour for B. the capacity of machining is 25 per hour for A and 40 per hour for B. The Casting for part A costs Rs.2 each and for B they cost Rs.3 each. They sell for Rs.5 and Rs.6 respectively. The three machines have running costs of Rs.20, Rs.14 and Rs.17.5 per hour rasp. Assuming that any combination of A and B can be sold, what product mix maximizes the profitability?
- April 2004
M/s.ABC is in jewellery business and is specialized in making of rings & bracelets of silver & gold. Making of one bracelet requires 1 unit of silver & 2 units of gold whereas making of one ring requires 3 units of silver & 1 unit of gold. The company has 9 units of silver & 8 units of gold with them. They earn profit of Rs.40 on each ring & Rs.50 on each bracelet. Determine the quantity of rings & bracelets, company should make to maximize their profitability.
- Oct 2004
Padma limited makes three different kinds of chairs. All can be made profitably in this company but the monthly production is constrained by the limited amount of labour, wood and screws available each month. The company will choose the combination of chairs that maximizes its revenue.
Input Arm Chair Executive Chair Officer Chair Monthly Availability
Labour Hours 12 7 9 1260
Wood 22 18 16 19008
Screws 2 4 3 396
Selling Price 4000 2000 5000
- Oct 2004
Hardware fabricators ltd. produces & sells three models of boilers. While market demand pose no restrictions, the capacity to produce is currently constrained by the limited supplies of special grade steel to 1500 kgs per week and machine processing time limited to 1200 hours per week. Model 1 requires 6 kgs of steel and 3 hours of machine processing .similarly these figures for model 2 are 3 kgs and 4 hours whereas for model 3 these figures are 5 kgs and 5 hours each. The profit contribution per boiler for these three models is Rs.60, Rs40 and Rs 80 respectively. Determine the optimal product mix to maximize the total profitability.
- April 2005
Product A offers Rs.25 per unit & product B offers a profit of Rs.40 per unit. To manufacture the products the raw materials-leather,wood & glue are required. To produce 1 unit of product A, 0.50 kgs of leather, 4 sq.meters of wood & 0.2 liters of glue is required whereas the requirement for B is 0.25 kgs of leather, 7 sq.meters of wood & 0.2 ltr.of glue. The total availability of the resources include 2200kgs of leather, 28000 sq.meters of wood & 1400 liters of glue. Determine the product mix to optimise the objective of the company.
- April 2005
R.K.Steel manufacturing company produces two items P1and P2.it uses sheet metal, equipment and labour. input –output relationship and resources available are as follows
Input Product Requirement Availability
P1 P2
Sheet Metal 1 Sq.Cm 1 Sq.Cm. 50 Sq.Cm.
Labour 1 Man Hour 2 Man Hours 80 Man Hours
Equipment 3 Hours 2 Hours 140 Hours
Profit In Rupees 4 Per Unit 3 Per Unit
How many units of P1 and P2 should be manufactured to maximize profitability of the company ?
- Oct 2005
The manager of an oil refinery must decide on the optimal mix of two possible blending processes of which the inputs & outputs per production run are as follows;
Process Inputs(Units) Output (Units)
Crude A Crude B Gasoline X Gasoline Y
1 5 3 5 8
2 4 5 4 4
The maximum amount available of crude A & B are 200 units & 150 units respectively. Market requirements show at least 100 units of gasoline X & 80 units of gasoline Y must be produced. The profits per production run for process 1 & 2 are Rs.300 & Rs.400 resp. Determine the product mix to optimise the profitability.
- Oct.2006
Suzan & co. Manufacturers two items x1 & x2. It purchases raw materials which are then processed on three machines. Per unit cost of raw material of item x1 & x2 are Rs.2 & Rs.3 resp. These items are sold in the market at Rs.5 & Rs.6 per unit resp. The running cost for the processing machine is Rs.20, Rs.14 & Rs.17.50 per hour respectively. The capacities of the machines are as given below
Machine Item X1 Item X2
A 25 / hr 40 /hr
B 28 / hr 35 / hr
C 35 / hr 25 / hr
Determine the quantities of products to be manufactured to maximize the profitability
- April 2007
A manufacturer produces two different models x & y of the same product. Model x makes a contribution of Rs.50 per unit and whereas model y makes Rs.30 per unit towards total profit. Raw materials r1 & r2 are required for production. At least 18 kgs of r1 and at least 12 kgs. Of r2 must be used. Also at most 34 labour hours are to be utilized. A quantity of 2 kgs of r1 is required for x and 1 kg of r1 is required for y. For each of x & y, 1 kg of r2 is required. It takes 3 labour hours to manufacture x and 2 labour hours to manufacture y. how many units of each model should be produced to maximise the profits.
- Oct 2007
Backbay Garments company manufacture shirts & blouses for western department store. Western department will accept all the production supplied by the company. The production process includes cutting, sewing and packaging. Backbay employs 25 workers in cutting department, 35 in sewing department and 5 in packaging department. The factory works 8 hours a day and 5 days a week. The following table gives time requirements and profits per unit for the two garments.
Garments Minutes Per Unit
Cutting Sewing Packaging Unit Profit (Rs.)
Shirts 20 70 12 2.50
Blouses 60 60 4 3.20
Determine the weekly optimal productionschedule to maximize the profitability.
- April 2008
A furniture manufacturer makes two products, chairs & tables. Processing of these products is done on two types of machine a b. A chair requires 2 hours on machine a & 6 hours on machine b. A table requires 5 hours on machine a no time on machine b. There are 16 hours per day available on machine a & 30 hours on machine b. Profit gained by the manufacturer from a chair and a table are Rs.2 and Rs.10 per unit respectively. What should be the daily production of each of the two products to maximize the total profitability?
- Oct 2008
XYZ company manufactures two products .To manufacture product A, a certain machine has to work for 1.5 hours and in addition a craftsman has to work for 2 hours. To manufacture product B, the machine has to work for 2.5 hours and craftsman has to work for 1.5 hours. In a week factory can avail of 80 hours of machine time and 70 hours of craftsman time. The profit on product A is Rs.50 per unit and on B it is Rs.40 per unit. If all the products produced can be sold away, find the quantity of each product to be produced for maximizing profitability of the company
- April 2009
A ) A confectioner sells 2 products A & B. the contribution of A is Rs.30 per unit and B is also contributing Rs.30 per unit. The products are produced in common production process.the production process has capacity of 30000 man hours. It takes 3 hours to manufacture a unit of A & 1 hour for a unit of B. The maximum of 8000 units of A can be sold & maximum of 12000 units of B can be sold. Formulate this as alpp to maximize contribution & solve either by simplex or graphical method.
B) explain with a graphical figure presence of a redundant constraint in a LPP.
- April 2010
ABC limited manufacture tables & Chairs. They have just acquired a new workshop that can operated 48 hours a week. Production of table will require 2 hours & a chair will require 3 hours of production time. Each table will contribute Rs.80 & a Chair contributes Rs.80 towards profits. The marketing department has determined that the maximum of 15 tables & 10 chairs can be sold every week. Formulate the LPP & determine the optimum product mix that will maximize profits for the company by using graphical or simplex method.
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