Page 1 : 12/03/2022, 18:04, , Plus Two Maths Chapter Wise Questions and Answers Chapter 12 Linear Programming – HSSLive Guru, , Menu, , HSSLive Guru, , Plus Two Maths Chapter Wise Questions and, Answers Chapter 12 Linear Programming, February 11, 2020 by Prasanna, , Students can Download Chapter 12 Linear Programming Questions and Answers, Plus, Two Maths Chapter Wise Questions and Answers helps you to revise the complete, Kerala State Syllabus and score more marks in your examinations., , Kerala Plus Two Maths Chapter Wise Questions and, Answers Chapter 12 Linear Programming, Plus Two Maths Linear Programming Four Mark Questions, and Answers, Question 1., Solve the following LPP Graphically;, Maximise; Z = 60x + 15y, Subject to constraints;, x + y ≤ 50, 3x + y ≤ 90, x ≥ 0, y ≥ 0., Answer:, 1. In the figure the shaded region OABC is the fesible region. Here the region is, bounded. The corner points are O(0, 0), A(30, 0), B(20, 30), C(0, 50)., , Given; Z = 60x + 15y, https://hssliveguru.com/plus-two-maths-chapter-wise-questions-and-answers-chapter-12/, , 1/10

Page 2 : 12/03/2022, 18:04, , Plus Two Maths Chapter Wise Questions and Answers Chapter 12 Linear Programming – HSSLive Guru, , Corner points, , Value of Z, , O, , Z=0, , A, , Z = 60(30) + 15(0) = 1800, , B, , Z = 60(20) + 15(30) = 1650, , C, , Z = 60(0) + 15(50) = 750, , Since maximum value of Z occurs at A, the soluion is Z = 1800, (30, 0)., , Question 2., Solve the following LPP Graphically;, Minimise; Z = -3x + 4y, Subject to constraints;, x + 2y ≤ 8, 3x + 2y ≤ 12, x ≥ 0, y ≥ 0, Answer:, In the figure the shaded region OABC is the fesible region. Here the region is, bounded. The corner points are O(0, 0), A(4, 0) B(2, 3), C(0, 4)., , Given; Z = -3x + 4y, Corner points, , Value of Z, , O, , Z=0, , A, , Z = -3(4) + 4(0) = -12, , B, , Z = -3(2) + 4(3) = 6, , C, , Z = -3(0) + 4(4) = 16, , https://hssliveguru.com/plus-two-maths-chapter-wise-questions-and-answers-chapter-12/, , 2/10

Page 3 : 12/03/2022, 18:04, , Plus Two Maths Chapter Wise Questions and Answers Chapter 12 Linear Programming – HSSLive Guru, , Since minimum value of Z occurs at A, the soluion is Z = -12, (4, 0)., , Question 3., Solve the following LPP Graphically;, Maximise; Z = 3x + 5y, Subject to constraints;, x + 3y ≥ 3, x + y ≥ 2, x ≥ 0, y ≥ 0, Answer:, In the figure the shaded region ABC is the fesible region. Here the region is, unbouded., , 3, , The corner points are A(3, 0), B( 2 ,, , 1, 2, , ), , , C(0, 2), , Given; Z = 3x + 5y, Corner points, , Value of Z, , A, , Z = 3(3) + 5(0) = 9, , B, , Z = 3( 2 ) + 5( 12 ) = 7, , C, , Z = 3(0) + 5(2) = 10, , 3, , 3, , Form the table, minumum value of Z is 7 at B( 2 ,, , 1, 2, , ), , . The feasible region is, , unbounded, so consider the inequality 3x + 5y < 7. Clearly the feasible region has no, common points with 3x + 5y < 7, Thus minimum value of Z occurs at B, the soluion is Z, = 7., , Plus Two Maths Linear Programming Six Mark Questions and, Answers, Question 1., One kind of a cake requires 200g of flour and 25g of fat, and another kind of cake, https://hssliveguru.com/plus-two-maths-chapter-wise-questions-and-answers-chapter-12/, , 3/10

Page 4 : 12/03/2022, 18:04, , Plus Two Maths Chapter Wise Questions and Answers Chapter 12 Linear Programming – HSSLive Guru, , requires 100g of flour and 50g of fat. Find the maximum number of cakes which can, be made from 5kg of flour and 1kg of fat assuming that there is no shortage of the, other ingredients, used in making the cake., Answer:, Let the number of cakes made of type I are x and that of type II are y. Then the total, number of cakes will be Z = x + y, Flour constraint 200x + 100y ≤ 5000, Fat constraint 25x + 50y ≤ 1000, Therefore;, Maximise; Z = x + y, 2x + y ≤ 50; x + 2y ≤ 40; x ≥ 0, y ≥ 0, , In the figure the shaded region OABC is the feasible region. Here the region is, bounded. The corner points are O(0, 0), A(25, 0), B(20, 10), C(0, 20), Given; Z = x + y, Corner points, , Value of Z, , O, , Z=0, , A, , Z = 25 + 0 = 25, , B, , Z = 20 + 10 = 30, , C, , Z = 0 + 20 = 20, , Since maximum value of Z occurs at B, the soluion is Z = 30, (20, 10)., , Question 2., A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of, machine and 3hours of craftman’s time in its making, while a cricket bat takes 3 hours, of machine time and 1 hour of craftman’s time. In a day, the factory has availability of, not more than 42 hours of machine time and 24 hours of craftman’s time., https://hssliveguru.com/plus-two-maths-chapter-wise-questions-and-answers-chapter-12/, , 4/10

Page 5 : 12/03/2022, 18:04, , Plus Two Maths Chapter Wise Questions and Answers Chapter 12 Linear Programming – HSSLive Guru, , 1. What no. of rackets and bats must be produced if the factory is to work at full, capacity?, 2. If the profit on a racket and a bat is 10 find maximum profit., Answer:, Let the number of rackets made = x and that of bats = y., Maximise; Z = x + y, Machine constraints 1.5x + 3y ≤ 42, Craftsman’s constraint 3x + y ≤ 24, Therefore; Maximise; Z = x + y, x + 2y ≤ 14, 3x + y ≤ 24, x ≥ 0, y ≥ 0, In the figure the shaded region OABC is the fesible region. Here the region is, bounded. The corner points are O(0, 0), A(8, 0), B(4, 10), C(0, 14)., , Given; Z = x + y, Corner points, , Value of Z, , O, , Z=0, , A, , Z=8+0=8, , B, , Z = 4 + 12 = 16, , C, , Z = 0 + 14 = 14, , Since maximum value of Z occurs at B, the soluion is Z = 16, (4, 12)., , Question 3., Two godowns A and B have grains capacity of 100 quintals and 50 quintals, respectively. They supply to 3 ration shops D, E, and F whose requirement are 60, 50, and 40 quintals respectively. The cost of transportation per quintal from the, https://hssliveguru.com/plus-two-maths-chapter-wise-questions-and-answers-chapter-12/, , 5/10

Page 6 : 12/03/2022, 18:04, , Plus Two Maths Chapter Wise Questions and Answers Chapter 12 Linear Programming – HSSLive Guru, , godowns to the shops is given in the following table; Transportation cost per, quintal(in Rs.), , Hence should the supplies be transported in order that the transportation cost is, minimum? What is the minimum cost?, Answer:, , Express the problem diagrammatically as shown above. The total transportation cost, is given by, Z = 6x + 3y + 2.5{100 – (x + y)} + 4(60 – x) + 2(50 – y) + 3(-60 + (x + y)), ⇒ Z = 2.5x + 1.5y + 410, 100 – (x + y) ≥ 0 ⇒ x + y ≤ 100, 60 – x ≥ 0 ⇒ x ≤ 60, 50 – y ≥ 0 ⇒ y ≤ 50 – 60 + x + y ≥ 0 ⇒ x + y ≥ 60, Then the given LPP is, Minimise; Z = 2.5x + 1.5y + 410, x + y ≤ 100, x + y ≥ 60, 0 ≤ x ≤ 60, 0 ≤ y ≤ 50, Plus Two Maths Linear Programming 6 Mark Questions and Answers 8, In the figure the shaded region ABCD is the feasible region. Here the region is, bounded. The corner points are, A(60, 0), B(60, 40), C(50, 50), D(10, 50)., Given; Z = 2.5x + 1.5y + 410, Corner points, , Value of Z, , A, , Z = 2.5(60) + 1.5(0) + 410= 560, , https://hssliveguru.com/plus-two-maths-chapter-wise-questions-and-answers-chapter-12/, , 6/10

Page 7 : 12/03/2022, 18:04, , Plus Two Maths Chapter Wise Questions and Answers Chapter 12 Linear Programming – HSSLive Guru, , B, , Z = 2.5(60) + 1.5(40) + 410 = 620, , C, , Z = 2.5(50) + 1.5(50) + 410 = 610, , D, , Z = 2.5(10) + 1.5(50) + 410 = 510, , Since minimum value of Z occurs at D, the soluion is Z = 510., , Question 4., (i) Choose the correct answer from the bracket. If an LPP is consistent, then its, feasible region is always, (a) Bounded, (b) Unbounded, (c) Convex region, (d) Concave region, (ii) Maximize Z = 2x + 3y subject to the constraints x + y ≤ 4, x ≥ 0, y ≥ 0., Answer:, (i) (c) Convex region., (ii), , Corner points of the feasible region are as follows, Corner points, , Z = 2x + 3y, , 0(0, 0), , 0, , A(0, 4), , 12 → Maximum, , B(4, 0), , 8, , ∴ the maximum value of Z is 12 attained at (0, 4)., https://hssliveguru.com/plus-two-maths-chapter-wise-questions-and-answers-chapter-12/, , 7/10

Page 8 : 12/03/2022, 18:04, , Plus Two Maths Chapter Wise Questions and Answers Chapter 12 Linear Programming – HSSLive Guru, , Question 5., The graph of a linear programming problem is given below. The shaded region is the, feasible region. The objective function is Z = px + qy, , 1. What are the co-ordinates of the comers of the feasible region., 2. Write the constraints, 3. If the Max. Z occurs at A and B, what is the relation between p and q?, 4. If q = 1, write the objective function, 5. Find the Max Z, Answer:, 1. Corner points are O(0, 0), A(5, 0), B(3, 4), C(0, 5)., 2. Constraints are 2x + y ≤ 10, x + 3y ≤ 15, x ≥ 0, y ≥ 0., 3. At (3, 4), Z = 3p + 4q, At (5, 0), Z = 5p, ⇒ 3p + 4q = 5p ⇒ p = 2q., 4. If q = 1, p=2, Then the objective function is,, Maximize Z = 2x + y., 5. At (3, 4) Z = 2 × 3 + 4 = 10 is the maximum value., , Question 6., A diet is to contain at least 80 units of vitamin A and 100 units of minerals. Two foods, F1 and F2 are available. Food F1 costs Rs 4 per unit food and F2 costs Rs 6 per unit., One unit of food F1 contains 3 units of vitamin A and 4 units of minerals. One unit of, https://hssliveguru.com/plus-two-maths-chapter-wise-questions-and-answers-chapter-12/, , 8/10

Page 9 : 12/03/2022, 18:04, , Plus Two Maths Chapter Wise Questions and Answers Chapter 12 Linear Programming – HSSLive Guru, , food F2 contains 6 units of vitamin A and 3 units of minerals. Formulate this as a, linear programming problem. Find the minimum costs for diet that consists of, mixture of these two foods and also meets the minimal nutritional requirements., Answer:, Let x units of food F1 and y units of food F2 be in the diet, Total cost Z = 4x + 6y, Then the LPP is, Minimize Z = 4x + 6, Subject to the constraints, 3x + 6y ≥ 80, 4x + 3y ≥ 100, x, y ≥ 0, , The feasible region is unbounded, , As the feasible region is unbounded, 104 may or may not be the minimum value of Z., For this we draw a graph of the inequality 4x + 6y < 104 or 2x + 3y < 52 and check, whether the resulting half plane has points in common with the feasible region or, not., It can be seen that the feasible region has no common points with 2x + 3y < 52, Therefore minimum cost of the mixture will be 104., Plus Two, Plus Two Maths Chapter Wise Questions and Answers Chapter 11 Three, Dimensional Geometry, https://hssliveguru.com/plus-two-maths-chapter-wise-questions-and-answers-chapter-12/, , 9/10

Page 10 : 12/03/2022, 18:04, , Plus Two Maths Chapter Wise Questions and Answers Chapter 12 Linear Programming – HSSLive Guru, , Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 5, Emerging Modes of Business, , Search …, , Recent Posts, HSSLive Plus Two Study Material / Question Bank Kerala, Plus One Malayalam Textbook Answers Unit 4 Chapter 6 Shasthrakriya, Plus One Accountancy Chapter Wise Questions and Answers Kerala, Plus One Economics Chapter Wise Questions and Answers Chapter 4 Presentation of, Data, Kerala Syllabus 9th Standard Maths Solutions Chapter 13 Statistics in Malayalam, Plus One Malayalam Textbook Answers Unit 4 Chapter 5 Samkramanam, Plus One Malayalam Textbook Answers Unit 4 Chapter 4 Vasanavikrithi, Plus One Physics Notes Chapter 5 Law of Motion, Kerala Syllabus 10th Standard Social Science Solutions Chapter 5 Culture and, Nationalism in Malayalam, Plus One Malayalam Textbook Answers Unit 4 Chapter 3 Muhyadheen Mala, Plus One Malayalam Textbook Answers Unit 4 Chapter 2 Anukampa, , Copyright © 2022 HSSLive Guru, , https://hssliveguru.com/plus-two-maths-chapter-wise-questions-and-answers-chapter-12/, , 10/10