{"id":21504,"date":"2020-01-27T16:13:37","date_gmt":"2020-01-27T10:43:37","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=21504"},"modified":"2021-07-02T15:26:31","modified_gmt":"2021-07-02T09:56:31","slug":"2nd-puc-maths-question-bank-chapter-12-ex-12-2","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/2nd-puc-maths-question-bank-chapter-12-ex-12-2\/","title":{"rendered":"2nd PUC Maths Question Bank Chapter 12 Linear Programming Ex 12.2"},"content":{"rendered":"

Students can Download Maths Chapter 12 Linear Programming Ex 12.2 Questions and Answers, Notes Pdf, 2nd PUC Maths Question Bank with Answers<\/a>\u00a0helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.<\/p>\n

Karnataka 2nd PUC Maths Question Bank Chapter 12 Linear Programming Ex 12.2<\/h2>\n

2nd PUC Maths Linear Programming NCERT Text Book Questions and Answers Ex 12.2<\/h3>\n

Question 1.
\nReshma wishes to mix two types of food P and Q in such a way that the vitamin contents of the mixture contain at least 8 units of vitamin A and 11 units of vitamin B. Food P costs \u20b9 60\/ kg and Food Q costs t 80\/kg. Food P contains 3 units\/kg of Vitamin A and 5 units \/ kg of Vitamin B while food Q contains 4 units\/kg of Vitamin A and 2 units\/kg of vitamin B. Determine the minimum cost of the mixture.
\nAnswer:
\n\"2nd
\nZ = 60x + 80y subject to
\n(i) 3x + 4y \u2265 8
\n(ii) 5x + 2y \u2265 11
\n\"2nd
\n\\(A\\left(\\frac{8}{3}, 0\\right) \\text { and } B\\left(2, \\frac{1}{2}\\right)\\). The minimum value lies in the line joining the points \\(\\left(\\frac{8}{3}, 0\\right) \\text { and } \\mathrm{B}\\left(2, \\frac{1}{2}\\right)\\)<\/p>\n

\"KSEEB<\/p>\n

Question 2.
\nOne kind of cake requires 200g of flour and 25g of fat, and another kind of cake requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes.
\nAnswer:
\n\"2nd
\nZ = x + y subject to the constraints
\n(i) 200 x + 100y \u2264 5000 \u21d2 2x + y <50
\n(ii) 25x + 50y \u2264 1000 \u21d2 x + 2y < 40
\n(iii) x , y \u2265 0
\n\"2nd
\nABCD is the solution region
\n\"2nd
\nA (0, 0 )\u00a0 Z = 0
\nB (25, 0)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Z = 25 + 0 = 25
\nC(20, 10)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Z = 20+10 = 30
\nD (0, 20)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Z = 0 + 20 = 20
\nAt C (20, 10) maximum number of cakes can be made.<\/p>\n

Question 3.
\nA factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman\u2019s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman\u2019s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman\u2019s time.
\n(i) What number of rackets and bats must be made if the factory is to work at full capacity?
\n(ii) If the profit on a racket and on a bat is \u20b9 20 and \u20b9 10 respectively, find the maximuin profit of the factory when it works at full capacity.
\nAnswer:
\n\"2nd
\nZ = x +y P = 20x +10 y
\nZ subject to constraints
\n(i) \\(\\frac{3}{2} x+3 y \\leq 42 \\quad x+2 y \\leq 28\\)
\n(ii) 3x + y \u2264 24
\n(iii) x \u2265 0; y \u2265 0
\n\"2nd
\nABCD is the solution region
\nA(0,0)\u00a0 \u00a0Z = 0\u00a0 P = 0
\n\"2nd
\nABCD is the solution region
\nA (0,0)\u00a0 \u00a0Z = 0\u00a0 \u00a0P = 0
\nB (8,0)\u00a0 \u00a0 Z = 8\u00a0 \u00a0 P=20 x 8 = \u20b9 160
\nC (4. 12)\u00a0 Z = 16\u00a0 P = \u20b9 200
\nD (0,14)\u00a0 \u00a0Z = 14\u00a0 P = \u20b9 140
\nAt C (4, 12) Z is maximised to 16 and then profit is also maximised by the manufacture of 4 rackets and 12 bats.<\/p>\n

\"KSEEB<\/p>\n

Question 4.
\nA manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to , produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts .He earns a profit of ? 17.50 per package on nuts and ? 7.00 per package on bolts. How many packages of each should be produced each day his machines for at the most 12 hours a day?
\nAnswer:
\n\"2nd
\n\\(P=\\frac{35}{2} x+7 y\\)
\n(i) x + 3y \u2264 12
\n(ii) 3x + y \u2264 12
\n(iii) x \u22650,y\u22650
\n\"2nd
\nABCD is the solution region A(0,0) P = 0
\n\"2nd
\nA (0,0) p = 0
\nB (4,0)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 P = 70 \u20b9 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0.
\nC (3, 3)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 P = 73.5 \u20b9
\nD (0, 4)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 P = 28 \u20b9
\nAt (3, 3) he can maximise his profit. By producing 3 packages of nuts and bolts each.<\/p>\n

Question 5.
\nA factory manufactures two types of screws, A and B. Each type of screw requires the use of two machines, an automatic and a hand operated. It takes 4 minutes on the automatic and 6 minutes on hand operated machines to manufacture a package of screws A, while it takes 6 minutes on automatic and 3 minutes on the hand operated machines to manufacture a package of screws B. Each machine is available for at the most 4 hours on any day. The manufacturer can sell a package of screws A at a profit of \u20b9 7 and screws B at a profit of \u20b9 10. Assuming that he can sell all the screws he manufactures, how many packages of each type should the factory owner produce in a day in order to maximise his profit? Determine the
\nAnswer:<\/p>\n\n\n\n\n\n\n
Time on<\/strong><\/td>\nA(x)<\/strong><\/td>\nB(y)<\/strong><\/td>\nTotal<\/strong><\/td>\n<\/tr>\n
(i) automatic machine<\/td>\n4 min<\/td>\n6 min<\/td>\n4 hrs<\/td>\n<\/tr>\n
(ii) Hand operated machine<\/td>\n6 min<\/td>\n3 min<\/td>\n4 hrs<\/td>\n<\/tr>\n
(iii) Profit<\/td>\n\u20b9 7<\/td>\n\u20b9 10<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

P = 7x +10y
\n\"2nd<\/p>\n

(i) 4x + 6y \u2264 240 \u21d2 2x + 3y \u2264120
\n(ii) 6x + 3y \u2264 240 \u21d2 2x + y \u2264 80
\n(iii) x \u2265 0 ; y \u2265 0
\n\"2nd<\/p>\n

ABCD is the solution region
\nA (0,0) P = 7 x 0+10 x 0 = 0
\nB (40, 0) P = 7 x\u00a0<\/sub>40+ 10 x 0 = 280 \u20b9
\nC (30, 20) P = 7 x 30+ 10 x 20 = 410 \u20b9
\nD (0, 40) P = 7 x 0+ 10 x 40 = 400 \u20b9
\nAt C (30,20)P is maximised
\n\u2234 30 types of screw A & 20 types of screw B.<\/p>\n

\"KSEEB<\/p>\n

Question 6.
\nA cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding\/cutting machine and a sprayer. It takes 2 hours on grinding\/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes 1 hour on the grinding\/ cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 hours and the grinding\/cutting machine for at the most 12 hours. The profit from the sale of a lamp is \u20b9 5 and that from a shade is \u20b9 3. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximise his profit?
\nAnswer:
\n\"2nd
\nP = 5x + 3y subject to the constraints
\n(i) 2x + y \u2264 12
\n(ii) 3x + 2y \u2264 20
\n(iii) x \u22650; y \u22650
\n\"2nd
\nABCD is the solution region
\n\"2nd
\nA(0,0) P= 0
\nB(6,0) P = 5 x 6+3 x 0 = 30 \u20b9
\nC(4,4) P = 5 x 4+3 x 4 = 32 \u20b9
\nD(0,10) P = 5 x 0+3 x 10 = 30 \u20b9
\nAt C (4, 4) p is maximised to\u00a0 32 \u20b9
\ni.e. 4 pedestal lamps and 4 wooden shades.<\/p>\n

\"KSEEB<\/p>\n

Question 7.
\nA company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A require 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and 8 minutes each for assembling. There are 3 hours 20 minutes available for cutting and 4 hours for assembling. The profit is \u20b9 5 each for type A and \u20b9 6 each for type B souvenirs. How many souvenirs of each type should the company manufacture in order to maximise the profit?
\nAnswer:
\n\"2nd
\nP = 5x + 6y
\nsubject to the constraints
\n\"2nd
\n(i) 5x + 8y \u2264 200
\n(ii) 10x + 8y \u2264 240 \u21d2 5x + 4y \u2264 120
\n(iii) x \u2265 0; y \u2265 0
\n\"2nd
\nA (0,0) P = 5x + 6y = 0
\nB (24,0) P = 5 x 24+ 6 x 0= 120 \u20b9
\nC (8,20) P = 5 x 8 + 6 x 20 = 160 \u20b9
\nD (0, 25) P = 5 x 0+ 6 x 25 = 150 \u20b9
\nAt C (8, 20) P is maximised to \u20b9 160
\n\u2234 8 types of A and 2 : 6 types of B<\/p>\n

Question 8.
\nA merchant plans to sell two types of personal computers a desktop model and a portable model that will cost \u20b9 25000 and \u20b9 40000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the number of units of each type of computers which the merchant should stock to get maximum profit if he does not want to invest more than \u20b9 70 lakhs and if his profit on the desktop model is \u20b9 4500 and on portable model is \u20b9 5000.
\nAnswer:
\n\"2nd
\nP = 4500 x + 5000 y subject to
\n(i) x + y \u2264 250
\n(ii) 25000 x + 40000 y \u2264 7000000
\n5x + 8y \u2264\u00a01400
\nx \u2265 0; y \u2265 0
\n\"2nd
\nABCD is the solution region
\n\"2nd
\nA (0,0), P = 4500 x + 5000 y = 0
\nB (250,0), P = 4500 x 250 = \u20b9 1125000
\nC (200,50), P = 4500 x 200 + 5000 x 50 = \u20b9 1150000
\nD (0,175), P = 5000 x 175 = \u20b9 875000
\n\u2234 The profit is maximised at C (200,50) \u20b9 1150000<\/p>\n

\"KSEEB<\/p>\n

Question 9.
\nA diet is to contain at least 80 units of vitamin A and 100 units of minerals. Two foods F1<\/sub> and F2<\/sub> are available. Food F2<\/sub> costs \u20b9 4 per unit food and F2<\/sub> costs \u20b9 6 per unit. One unit of food F1<\/sub> contains 3 units of vitamin A and 4 units of minerals. One unit of food F2<\/sub> contains 6 units of vitamin A and 3 units of minerals. Formulate this as a linear programming problem. Find the minimum cost for diet that consists of mixture of these two foods and also meets the minimal nutritional requirements.
\nAnswer:
\n\"2nd
\nMinimize Z = 4x + 6y
\n(i) 3x + 6y \u2265 80
\n(ii) 4x + 3y \u2265100
\n(iii) x \u2265 0 ; y \u2265 0
\n\"2nd
\n\"2nd<\/p>\n

Question 10.
\nThere are two types of fertilisers F1<\/sub> and F2 .<\/sub>F1<\/sub> consists of 10% nitrogen and 6% phosphoric acid and F2<\/sub> consists of 5 % nitrogen and 10% phosphoric acid. After testing the soil conditions, a farmer finds that she needs atleast 14 kg of nitrogen and 14 kg of phosphoric acid for her crop. If F1<\/sub> costs \u20b9 6\/kg and F2<\/sub> costs \u20b9 5\/kg, determine how much of each type of fertiliser should be used so that nutrient requirements are met at a minimum cost. What is the minimum cost?
\nAnswer:
\n\"2nd
\nB (100,80) Z=1000
\nC (0,280) Z = 1400
\nCost is minimum at B (100, 80)
\n\u2234 F1 <\/sub>= 100\u00a0 \u00a0F2<\/sub> = 80<\/p>\n

\"KSEEB<\/p>\n

Question 11.
\nThe corner points of the feasible region determined by the following system of linear inequalities:
\n2x + y \u2264 10, x + 3y \u2264 15, x, y \u2265 0 are (0, 0), (5, 0), (3, 4) and (0, 5). Let Z = px + qy, where p, q >0 . Condition on p and q so that the maximum of Z occurs at both (3, 4) and (0, 5) is.
\n(A) p = q
\n(B) P = 2q
\n(C) p = 3q
\n(D) q = 3p
\nAnswer:
\nAt (0, 0)\u00a0 Z = 0
\nAt (5, 0)\u00a0 Z = 5p
\nAt (3, 4)\u00a0 Z = 3p +4q
\nAt (0, 5)\u00a0 Z = 5q
\n\u2234 maximum of Z
\n3p + 4q = 5q
\n\u2234 3p = q
\nAnswer is (D) q = 3p<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can Download Maths Chapter 12 Linear Programming Ex 12.2 Questions and Answers, Notes Pdf, 2nd PUC Maths Question Bank with Answers\u00a0helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations. Karnataka 2nd PUC Maths Question Bank Chapter 12 Linear Programming Ex 12.2 2nd PUC Maths Linear Programming …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[82],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/21504"}],"collection":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/comments?post=21504"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/21504\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=21504"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=21504"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=21504"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}