The summaries provide the key details and constraints of linear programming problems presented in the question papers from the last 5 years: 1) Multiple choice questions asking to solve linear programming problems involving constraints on production quantities to maximize profit for companies producing different products. 2) Questions involving constraints on machine hours, labor hours, and material availability to maximize production or minimize costs for companies producing various goods. 3) Graphical representation questions asking to determine optimal production quantities given profit margins and constraints to maximize total profit. 4) Nutrition-based linear programming problems with constraints on meeting minimum nutrient requirements to determine optimal quantities of foods to purchase at lowest cost.

1. Last 5 year Question Paper
2018-19
The probabilitythata contractor will getacontract forroad constructionin4/9 and the probabilitythathe will
getcontract forthe constructionof a watertank is5/7. What isthe probabilityof getting1) at leastone of the
contracts 2) boththe contracts 3) exactone contract?
Or
The odds againstA solvingaproblemare 8 to 6 and the oddsinfavor of B solvingthe same problemare 14 to
10. What isthe probabilitythatif bothof themtriesthe problemwouldbe solved?
2017-18
A bag contains5 black 7 white balls.A ball isdrawnout of it and replacedinthe bag.Thena ball isdrawn
again.What is the probabilitythat1) boththe ballsdrawnwere black2) both were white 3) the firstball was
white andthe secondblack4) the firstsball wasblackand the secondwhite.
or
The J. K. Corp Ltd.,has 40 female employeesand60 male employees.If twoemployeesare selectedat
random,whatis the probabilitythat – bothwill be males,bothwill be females,there will be one of each
gender.
2016-17
A Sub-Committee of 6membersistobe formedoutof a group consistingof 7 menand 4 ladies.Calculatethe
probabilitythatthe subcommittee will consistof (i) exactly2ladies,and(ii) atleast2 ladies.
or
There are 3 economists,4engineers,2statisticiansand1doctor. A committee of 4from amongthemis to be
formed.Findthe probabilitythatthe committee- (i) consistone of eachkind;(ii) hasatleastone economist;
(ii) hasthe doctor as a memberandthree others.
2015-16
One bag contains4 white and2 blackballs.Anothercontains3white and5 blackballs.If one ball isdrawn
fromeach bag, findthe probabilitythat – (i) bothare white;(ii) bothare black,and(iii) one iswhiteandone is
black.
or
The probabilitythata contractor will getaplumbingcontractis2/3 and the probabilitythathe will notgetan
electriccontractis 5/9. If the probabilityof gettingatleastone contractis4/5, whatis the probabilitythathe
will getboth?
2014-15
A Universityhastoselectanexaminerfromalistof 50 persons20 of themwomen30 men.10 of them
knowingHindi and40 not. 15 of thembeingteachersandthe remaining35not. What isthe probabilityof the
UniversityselectingaHindi-knowingWomanteacher?
or
Three groupworkerscontain3 menandone woman,2 menand twowomenand1 man and 3 women
respectively.One workerisselectedatrandomfromeach group.What isthe probabilitythatthe group
selectedconsistof 1man and 2 women?

2. . Last 5 year Question Paper
2018-19
1. A random sample of the heights of 81 students from a large population of students in Andhra University having S.D.
of 0.72 ft. has an average height of 5.5 ft. Find 99% confidence limits for the average. [Ans: 5.3432 & 5.6568]
2. A simple random of size 64 is drawn from a finite population consisting of 122 units. If the population S.D is 16.8,
find the standard error of sample mean when the sample is drawn (i) With replacement (II) Without replacement.
[Ans: 2.1; 1.45]
2017-18
3. A simple random sample of size 16 is drawn without replacement from a finite population consisting of 50 units. If
the number of defective units in the population be 5, find the standard error of the sample proportion of defectives.
[Ans: 0.0625]
4. A random sample of 400 oranges was taken from a large consignment and 52 where found to be defective. Show that
the standard error of the proportion of defective ones in a sample of this size is nearly 0.017.
2016-17
5. A simple random sample of size 5 is drawn without replacement from a finite population consisting of 41 units. If the
population S.D is 6.25, find the standard error of sample mean.(Use finite population correction). [Ans: 2.65]
6. An examination was given to 50 students of a college A and to 60 students at College B. At A, the mean grade was 75
with a standard deviation of 9. At B the mean grade was 79 with a standard deviation of &. Is there a significant
difference between the performance of the students at A and those at B, given that 5% and 1% significant? [Ans: Z
=2.56; Rejected and Accepted]
2015-16
7. The sales manager of a large company conducted a sample survey in States Orissa and Andhra taking 400 sample
salesmen in each case. Average sales in Orissa 2,500 and S.D. 400; Average sales in Andhra 2,200 and S.D. 550.
Test whether the average sales is the same in the two states at 1% level. [Ans: 8.82; Reject]
8. In a Rayagada district, 450 persons were considered regular consumers of tea out of a sample of 1000 persons. In
Koraput district, 400 were regular consumers of tea out of a sample of 800 persons. Do these facts reveal a significant
difference between the two districts as far as tea-drinking habit is concerned? (Use 5%) [Ans: --2.1097; Reject]
2014-15
9. Two groups A & B consist of 100 people each who have a disease. A serum is given to group A not to group B. It is
found that in groups A & B, 75 and 65 people respectively recover fromthe disease. Test the hypothesis that the serum
helps to cure the disease. [Ans: 1.54; Accept]
10. A group of 5 patients treated with medicine A weigh 42, 39, 48, 60 .and 41 kgs; a 2nd group of 7 patients from the
same hospital treated with medicine B weigh 38, 42, 56, 64, 68, 69 and 62 kgs. Do you agree with claim that medicine
‘B’ increases the weight significantly? [The value of t at 5% level of significance for 10 degree of freedom is 2.2281]

3. Last 5year question paper
2018-19
Q.1 . Maximize: P = X1 + 2X2 + 3X3 − X4
Constrains: X1 + 2X2 + 3X3 = 15
2X1 + X2 + 5X3 = 20
X1 + 2X2 + X3 + X4 = 10
None negative: X1 , X2 , X3 , and X4 ≥ 0
A firm produces two types of mats. Each mat of the first type needs twice as much labour as the second
type. If all the mats are of the second type only, the firm can produce a total of 500 units of mats a day.
The market limits daily sales of the first and second type to 150 and to 250 respectively. Assuming that
the profit per mat re `8 and `5 respectively for the two types, formulate the problem in a linear
programming model to determine the number of mats to be produced of each type so as to maximize the
profit.
2017-18
Q.2 A drug manufacturing company proposes to prepare a production plan for the medicines, X and Y.
there are sufficient ingredients available to make 20000 bottles of the medicine, X and 40000 bottles of
the medicine Y but there are only 45000 bottles into which either of the medicines can be filled in. it takes
3 hours to prepare sufficient materials to fill 1000 bottles of the medicine, X and one hour to prepare
enough materials to fill 1000 bottles of the medicine, Y and there are only 66 hours for this operation.
The profit is `8 per bottle for the medicine, X and `7 per bottle for the medicine, Y. From the above
formulate the problem as an LPP.
A firm produces two types of toy A & B. A takes twice as much as to produce as B and the firm has time to
produce a maximum of 2000 per day. The supply of plastic is sufficient to produce 1500 toys per day
(both A & B). B requires a fancy dress of which there are only 600 per day available. If the firm makes a
profit or `3 and `5 per toy respectively, as A & B, then how many of each toy should be produced per day
in order to maximize the total profit. Solve this problem using the graphic method.
2016-17
q.3 A Factory produces two articles, C & D. For C, machine hour required are 1.5 hours and a craftsman has to work
for 2 hours. For D, machine hours required are 2.5 hours, and a 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 of C is `5 and
that on each article of D is `4 if all the articles produced can be sold off, find graphically how many of each kind
should be produced to earn the maximum profit per week?
Max. Profit: P = 22X1 + 18X2
Constraints: 36X1 + 24X2 ≤ 576
X1 + X2 ≤ 20
Non-negative function: X1, X2 ≥ 0

4. 2015-16
A cold drink company has two bottling plant, located at two different places. Each plant produces three different
drinks, P, Q, & R. The capacity of the two plants in number of bottles per day are as follows:
Plant Products
P Q R
I
II
3000
1000
1000
1000
2000
6000
A market survey indicates that during any particular month there will be a demand for 24000 bottles of P, 16000
bottles of Q, and 48000 bottles of R. the operating cost per day of running the plants I and II are respectively 600
monetary units and 400 monetary units. How many days should the company run each plant during the month so
that the production cost is minimized while still meeting the market demand?
A firm is engaged in breeding the pigs. The pigs are fed on various products grown on the firm. Because of the need
to ensure certain nutrient constituents it is necessary to buy additional one or two products which we shall call P
and Q. the nutrient constituents (Vitamins and Proteins) in each unit of the products are given below.
Nutrients Nutrient constituent Min.
requirementP Q
1
2
3
36
3
20
6
12
10
108
36
100
Product, P costs RS. 20 per unit, and product, Q costs `40 per unit. Determine how much of products, P and Q must
be purchased so as to provide the pig with the nutrients not less than the minimum required, at the lowest possible
cost. Solve the problem graphically.
2014-15
A firm must produce 200 kgs, of a mixture consisting of the ingredients, P and Q which cost `3 and `8 per kg,
respectively. Not more than 80 kgs, of P can be used and at least 60 kgs., of Q must be used. Find by the simplex
method how much of each ingredient should be used in order to minimize the cost.
A diet for a patient should contain at least 4000 units of vitamins, 50 units of minerals and 1400 units of calories.
Two foods P and Q are available at a cost of `4 and `3 per unit respectively. If one unit of P contains 200 units of
vitamins, 1 unit of minerals and 40 units of calories and one unit of Q contains 100 units of vitamins, 2 units of
minerals and 40 units of calories. Find number of kgs required in respect of P and Q