**LINEAR PROGRAMMING PROBLEMS **

Q.34 A dietician wishes to mix two types of food in such a way that the vitamin content of the mixture contain at least 8 unit of vitamin A and 10 unit of vitamin C. Food I contains 2unit/kg of vitamin A and 1unit/kg of vitamin C, while food II contains I unit/kg of vitamin A and 2unit/kg of vitamin C. It cost Rs.5.00 per kg to purchase food I and Rs.7.00 per kg to produce food II. Determine the minimum cost of the mixture. Formulate the LPP and solve it. Why a person should take balanced food?

Q.35 A farmer has a supply of chemical fertilizers of type ‘ A ‘ which contains 10% nitrogen and 6% phosphoric acid and type ‘ B ‘ contains 5% of nitrogen and 10% of phosphoric acid. After soil testing it is found that at least 7kg of nitrogen and same quantity of phosphoric acid is required for a good crop. The fertilizers of type A and type B cost Rs.5 and Rs.8 per kilograms respectively. Using L .P.P, find how many kgs of each type of fertilizers should be bought to meet the requirement and cost be minimum solve the problem graphically. What are the side effects of using excessive fertilizers?

Q.36 If a class XII student aged 17 years, rides his motor cycle at 40km/hr, the petrol cost is Rs. 2per km. If he rides at a speed of 70km/hr, the petrol cost increases Rs.7per km. He has Rs.100 to spend on petrol and wishes to cover the maximum distance within one hour.

1. Express this as an L .P.P and solve graphically.

2. What is benefit of driving at an economical speed?

3. Should a child below 18years be allowed to drive a motorcycle? Give reasons

Q.37 Vikas has been given two lists of problems from his mathematics teacher with the instructions to submit not more than 100 of them correctly solved for marks. The problems in the first list are worth 10 marks each and those in the second list are worth 5 marks each. Vikas knows from past experience that he requires on an average of 4 minutes to solve a problem of 10 marks and 2 minutes to solve a problem of 5 marks. He has other subjects to worry about; he cannot devote more than 4 hours to his mathematics assignment. With reference to manage his time in best possible way how many problems from each list shall he do to maximize his marks? What is the importance of time management for students?

Q.38 An NGO is helping the poor people of earthquake hit village by providing medicines. In order to do this they set up a plant to prepare two medicines A and B. There is sufficient raw material available to make 20000 bottles of medicine A and 40000 bottles of medicine B but there are 45000 bottles into which either of the medicine can be put. Further it takes 3 hours to prepare enough material to fill 1000 bottles of medicine A and takes 1 hour to prepare enough material to fill 1000 bottles of medicine B and there are 66 hours available for the operation. If the bottle of medicine A is used for 8 patients and bottle of medicine B is used for 7 patients. How the NGO should plan his production to cover maximum patients? How can you help others in case of natural disaster?

Q.39 Probability of winning when batting coach A and bowling coach B working independently are 1/2 and 1/3 respectively. If both try for the win independently find the probability that there is a win. Will the independently working may be effective? And why?

Q.40 A person has undertaken a construction job. The probabilities are 0.65 that there will be strike, 0.80 that the construction job will be completed on time if there is no strike and 0.32 that the construction job will be completed on time if there is strike. Determine the probability that the construction job will be completed on time. What values are driven by this question?

Q.41 A clever student used a biased coin so that the head is 3 times as likely to occur as tail. If the coin tossed twice find the probability distribution and mean of numbers of tails. Is this a good tendency? Justify your answer.

Q.42 A man is known to speak truth 5 out of 6 times. He draws a ball from the bag containing 4 white and 6 black balls and reports that it is white. Find the probability that it is actually white? Do you think that speaking truth is always good?

Q.43 A drunkard man takes a step forward with probability 0.6 and takes a step backward with probability 0.4. He takes 9 steps in all. Find the probability that he is just one step away from the initial point. Do you think drinking habit can ruin one’s family life?

Q.44 If group A contains the students who try to solve the problem by knowledge, Group B contains the students who guess to solve the problem Group C contains the students who give answer by cheating. If n (A) = 20, n (B) = 15, n(C) = 10, 2 Students are selected at random. Find the probability that they are from group c. Do you think that cheating habit spoils the career?

**LINEAR PROGRAMMING PROBLEMS **

Q.45 In a school, 30% of the student has 100% attendance. Previous year result report tells that 70% of all students having 100% attendance attain A grade and 10% of remaining students attain A grade in their annual examination. At the end of the year, One student is chosen at random and he has an A grade. What is the probability that the student has 100% attendance? Also state the factors which affect the result of a student in the examination.

Q.46 A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is six. Find the probability that it is actually a six. Write any three benefits of speaking the truth.

Q.47 There are 20 People in a group. Out of them 7 people are non – vegetarian , 2 people are selected randomly. Write the probability distribution of non-vegetarian people. Explain whether you would like to be vegetarian or non- vegetarian and why ? Also keeping life of animals in mind how would you promote a person to be vegetarian?

Q.48 Two third of the students in a class are sincere about their study and rest are careless Probability of passing in examination are 0.7 and 0.2 for sincere and careless students respectively, A Student is chosen and is found to be passed what is the probability that he/she was sincere. Explain the importance of sincerity for a student.

Q.49 A company has two plants of scooter manufacturing. Plant I manufacture 70% Scooter and plant II manufactures 30%. At plant I 80% of the scooter’s are maintaining pollution norms and in plant II 90% of the scooter maintaining Pollution norms. A Scooter is chosen at random and is found to be fit on pollution norms. What is the probability that it has come from plant II. What is importance of pollution norms for a vehicle?

Q.50 A chairman is biased so that he selects his relatives for a job 3 times as likely as others. If there are 3 posts for a job. Find the probability distribution for selection of persons other than their relatives. If the chairman is biased than which value of life will be demolished ?

Q.51 A manufacturer has three machine operators A (skilled) B (Semi- skilled) and C (nonskilled). The first operator A Produces 1% defective items where as the other two operators B and C produces 5% and 7 % defective items respectively. A is on the job for 50% of time B in the job for 30% of the time and C is on the job for 20 % of the time. A defective item is produced what is the probability that it was produced by B? What is the value of skill?

Q.52 In a group of 100 families, 30 families like male child, 25 families like female child and 45 families feel both children are equal. If two families are selected at random out of 100 families, find the probability distribution of the number of families feel both children are equal. What is the importance in the society to develop the feeling that both children are equal?

Q.53 In a group of 200 people, 50% believe in that anger and violence will ruin the country, 30% do not believe in that anger and violence will ruin the country and 20% are not sure about anything. If 3 people are selected at random find the probability that 2 people believe and 1 does not believe that anger and violence will ruin the country. How do you consider that anger and violence will ruin the country?

Q.54 In a group of students, 200 attend coaching classes, 400 students attend school regularly and 600 students study themselves with help of peers. The probability that a student will succeed in life who attend coaching classes, attend school regularly and study themselves with help of peers are 0.1, 0.2 and 0.5 respectively. One student is selected who succeeded in life, what is the probability that he study himself with help of peers. What type of study can be considered for the success in life and why?