{"id":37749,"date":"2021-03-12T00:43:14","date_gmt":"2021-03-12T06:13:14","guid":{"rendered":"https:\/\/tnboardsolutions.com\/?p=37749"},"modified":"2021-07-08T01:54:20","modified_gmt":"2021-07-08T07:24:20","slug":"samacheer-kalvi-12th-business-maths-guide-chapter-10-miscellaneous-problems","status":"publish","type":"post","link":"https:\/\/tnboardsolutions.com\/samacheer-kalvi-12th-business-maths-guide-chapter-10-miscellaneous-problems\/","title":{"rendered":"Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems"},"content":{"rendered":"

Tamilnadu State Board New Syllabus\u00a0Samacheer Kalvi 12th Business Maths Guide<\/a> Pdf Chapter 10 Operations Research Miscellaneous Problems Text Book Back Questions and Answers, Notes.<\/p>\n

Tamilnadu Samacheer Kalvi 12th Business Maths Solutions Chapter 10 Operations Research Miscellaneous Problems<\/h2>\n

Question 1.
\nThe following table summarizes the supply, demand and cost information for four factors S1<\/sub>, S2<\/sub>, S3<\/sub>, S4<\/sub> Shipping goods to three warehouses D1<\/sub>, D2<\/sub>, D3<\/sub>.
\n\"Samacheer
\nFind an initial solution by using north west corner rule. What is the total cost for this solution?
\nSolution:
\nThe given transportation table is
\n\"Samacheer
\nHere total supply = 5 + 8 + 7+14 = 34
\nTotal amount =7 + 9 + 18 = 34
\n(i.e) Total supply = Total demand.
\n\u2234 The given problem is balanced transformation problem.
\nWe can find an initial basic feasible solution to the given problem.
\nFirst allocation:
\n\"Samacheer
\n\"Samacheer
\n\"Samacheer
\nTransportation schedule:
\nS1<\/sub> \u2192 D1<\/sub>; S2<\/sub> \u2192 D1<\/sub>; S2<\/sub> \u2192 D2<\/sub>;
\nS3<\/sub> \u2192 D2<\/sub>; S3<\/sub> \u2192 D3<\/sub>; S4<\/sub> \u2192 D3<\/sub>
\nThe transportation cost:
\n= (5 \u00d7 2) + (2 \u00d7 3) + (6 \u00d7 3) + (3 \u00d7 4) + (4 \u00d7 7) + (14 \u00d7 2)
\n= 10 + 6 + 18 + 12 + 28 + 28
\n= 102<\/p>\n

\"Samacheer<\/p>\n

Question 2.
\nConsider the following transportation problem
\n\"Samacheer
\nDetermine an initial basic feasible solution using (a) Least cost method (b) Vogel’s approximation method.
\nSolution:
\n(a) Least cost method
\nGiven transportation table is
\n\"Samacheer
\nTotal Availability = Total Requirement = 100
\n\u2234 The given problem is balanced transformation problem.
\nHence there exists a feasible solution to the given problem
\nFirst allocation:
\n\"Samacheer
\n\"Samacheer
\n\"Samacheer
\nHere
\nx12<\/sub> = 10; x13<\/sub> = 20; x21<\/sub> = 30;
\nx22<\/sub> = 10; x24<\/sub> = 10; x32<\/sub> = 20
\nTransportation Scheme:
\nO1<\/sub> \u2192 D2<\/sub>; O1<\/sub> \u2192 D3<\/sub>; O2<\/sub> \u2192 D1<\/sub>;
\nO2<\/sub> \u2192 D2<\/sub>; O2<\/sub> \u2192 D4<\/sub>; O3<\/sub> \u2192 D2<\/sub>
\nThe transportation cost:
\n=(10 \u00d7 8) + (20 \u00d7 3) + (30 \u00d7 4) + (10 \u00d7 5) + (10 \u00d7 4) + (20 \u00d7 2)
\n= 80 + 60 + 120 + 50 + 40 + 40
\n= 390<\/p>\n

(ii) Vogel’s approximation method:
\nHere \u03a3ai = \u03a3bj = 100
\n\u2234 The given problem is balanced transformation problem.
\nHence there exists a feasible solution to the given problem
\nFirst allocation:
\n\"Samacheer
\n\"Samacheer
\n\"Samacheer
\nHere
\nx11<\/sub> = 30; x13<\/sub> = 20; x22<\/sub> = 20;
\nx24<\/sub> = 10; x32<\/sub> = 20
\nTransportation Scheme:
\nO1<\/sub> \u2192 D1<\/sub>; O2<\/sub> \u2192 D3<\/sub>; O2<\/sub> \u2192 D2<\/sub>;
\nO2<\/sub> \u2192 D4<\/sub>; O3<\/sub> \u2192 D2<\/sub>;
\nTotal transportation cost:
\n= (30 \u00d7 5) + (20 \u00d7 3) + (20 \u00d7 5) + (10 \u00d7 4) + (20 \u00d7 2)
\n= 150 + 60 + 100 + 40 + 40
\n= 390<\/p>\n

\"Samacheer<\/p>\n

Question 3.
\nDetermine an initital basic feasible solution to the following transportation problem by using (i) North West Corner rule (ii) least cost method.
\n\"Samacheer
\nSolution:
\n(i) North West Corner rule:
\nThe given transportation table is
\n\"Samacheer
\nTotal supply = 25 + 35 + 40 = 100
\nTotal Requirement = 30 + 25 + 45 + 100
\n(i.e) Total supply = Total requirement.
\n\u2234 The given problem is balanced transformation problem.
\nHence there exists a feasible solution to the given problem
\nFirst allocation:
\n\"Samacheer
\n\"Samacheer
\nTransformation schedule:
\nS1<\/sub> \u2192 D1<\/sub>; S2<\/sub> \u2192 D1<\/sub>; S2<\/sub> \u2192 D2<\/sub>;
\nS3<\/sub> \u2192 D3<\/sub>; S3<\/sub> \u2192 D3<\/sub>;
\nThe transformation cost:
\n= (25 \u00d7 9) + (5 \u00d7 6) + (25 \u00d7 8) + (5 \u00d7 4) + (40 \u00d7 9)
\n= 225 + 30 + 200 + 20 + 360 = 835<\/p>\n

(ii) Least cost method
\nThe given transportation table is
\n\"Samacheer
\n(i.e) Total supply = Total requirement = 100
\n\u2234 The given problem is balanced transformation problem.
\nHence there exists a feasible solution to the given problem
\nFirst allocation:
\n\"Samacheer
\n\"Samacheer
\nTransportation schedule:
\nS1<\/sub> \u2192 D3<\/sub>; S2<\/sub> \u2192 D3<\/sub>; S3<\/sub> \u2192 D1<\/sub>
\nS3<\/sub> \u2192 D2<\/sub>;
\nThe transportation cost:
\n= (10 \u00d7 5) + (35 \u00d7 4) + (15 \u00d7 7) + (25 \u00d7 6) + (40 \u00d7 9)
\n= 50 + 140 + 105 + 150 + 360 = 805<\/p>\n

\"Samacheer<\/p>\n

Question 4.
\nExplain Vogel’s approximation method by obtaining initial basic feasible solution of the following transportation problem.
\n\"Samacheer
\nSolution:
\nThe given transportation table is
\n\"Samacheer
\nHere \u03a3ai = \u03a3bj =17
\n(i.e) Total supply = Total Demand
\n\u2234 The given problem is balanced transformation problem.
\nHence there exists a feasible solution to the given problem
\nFirst allocation:
\n\"Samacheer
\n\"Samacheer
\n\"Samacheer
\nHere
\nx11<\/sub> = 1; x12<\/sub> = 5; x24<\/sub> = 1;
\nx31<\/sub> = 6; x33<\/sub> = 15;
\nTransportation schedule:
\nO1<\/sub> \u2192 D1<\/sub>; O1<\/sub> \u2192 D2<\/sub>; O2<\/sub> \u2192 D4<\/sub>
\nO3<\/sub> \u2192 D1<\/sub>; O3<\/sub> \u2192 D3<\/sub>
\nThe transportation cost:
\n=(1 \u00d7 2) + (5 \u00d7 3) + (1 \u00d7 1) + (6 \u00d7 5) + (3 \u00d7 15) + (1 \u00d7 9)
\n= 2 + 15 + 1 + 30 + 45 + 9
\n= 102<\/p>\n

\"Samacheer<\/p>\n

Question 5.
\nA car hire company has one car at each of five depots a,b,c,d and e. A customer in each of the fine towers A, B, C, D and E requires a car. The distance (in miles) between the depots (origins) and the towers (destinations) where the customers are given the following distance matrix.
\n\"Samacheer
\nHow should the cars be assigned to the customers so as to minimize the distance travelled?
\nSolution:
\nHere the number of rows and columns are equal.
\n\u2234 The given assignment problem is balanced.
\nStep 1.
\nSelect the smallest element in each row and subtract this from all the elements in its row.
\n\"Samacheer<\/p>\n

Step 2.
\nSelect the smallest element in each column and subtract this from all the elements in its column.
\n\"Samacheer<\/p>\n

Step 3. (Assignment)
\nExamine the rows with exactly one zero, mark the zero by \u25a1 mark other zeros, in its column by X
\n\"Samacheer<\/p>\n

Step 4.
\nNow Examine the rows with exactly one zero, mark the zero by \u25a1 mark other zeros, in its column by X
\n\"Samacheer<\/p>\n

Step 5.
\nCover all the zeros of table 4 with three lives. Since three assignments were made please note that check [\u2713] Row C and E which have no assignment.
\n\"Samacheer<\/p>\n

Step 6.
\nDevelop the new revised tableau. Examine those elements that are not covered by a line in Table 5. Take the smallest element in each row and subtract from the uncovered cells, depots
\n\"Samacheer<\/p>\n

Step 7.
\nGo to step 3 and repeat the procedure until you arrive at an optimal assignments.
\ndepots<\/p>\n

Step 8.
\nDetermine an assignment
\n\"Samacheer
\nHere all the five assignments have been made. The optimal assignment schedule and total distance is
\n\"Samacheer
\n\u2234 The optimum Distance (minimum) 575 kms<\/p>\n

\"Samacheer<\/p>\n

Question 6.
\nA natural truck – rental service has a surplus of one truck in each of the cities 1, 2, 3, 4, 5 and 6 and a deficit of one truck in each of the cities 7, 8, 9, 10, 11 and 12. The distance (in kilometers) between the cities with a surplus and the cities with
\n\"Samacheer
\nHow should the truck be dispersed so as to minimize the total distance travelled?
\nSolution:
\nHere the number of rows and columns are equal.
\n\u2234 The given assignment problem is balanced.
\nStep 1.
\nSelect the smallest element in each row and subtract this from all the elements in its row.
\n\"Samacheer<\/p>\n

Step 2.
\nSelect the smallest element in each column and subtract this from all the elements in its column.
\n\"Samacheer<\/p>\n

Step 3.
\nExamine the rows with exactly one zero, mark the zero by \u25a1 mark other zeros, in its column by X
\n\"Samacheer<\/p>\n

Step 4.
\nExamine the Columns with exactly one zero. If there is exactly one zero, mark that zero by \u25a1 mark other zeros in its rows by X
\n\"Samacheer<\/p>\n

Step 5.
\nCover all the zeros of table 4 with five lines. Since three assignments were made
\n\"Samacheer<\/p>\n

Step 6.
\nDevelop the new revised tableau. Examine those elements that are not covered by a line in Table 5. Take the smallest element. This is l(one) in our case. By subtracting 1 from the uncovered cells.
\n\"Samacheer<\/p>\n

Step 7.
\nGo to step 3 and repeat the procedure until you arrive at an optimal assignments.<\/p>\n

Step 8.
\nDetermine an assignment
\n\"Samacheer
\nHere all the six assignments have been made. The optimal assignment schedule and total distance is
\n\"Samacheer
\n\u2234The optimum Distance (minimum) = 125 kms<\/p>\n

\"Samacheer<\/p>\n

Question 7.
\nA person wants to invest in one of three alternative investment plans: Stock, Bonds and Debentures. It is assumed that the person wishes to invest all of the funds in a plan. The pay – off matrix based on three potential economic conditions is given in the following table
\n\"Samacheer
\nSolution:
\n\"Samacheer
\n(i) Maximin
\nMax (3000, 1000, 6000) = 6000. Since the maximum pay of is 6000, the alternative ‘Debentures’, is selected.<\/p>\n

(ii) Minimax
\nMin (10000, 8000, 6000) = 6000, Since the minimum pay-off is 6000. the alternative ‘Debentures’ is selected.<\/p>\n

\"Samacheer<\/p>\n","protected":false},"excerpt":{"rendered":"

Tamilnadu State Board New Syllabus\u00a0Samacheer Kalvi 12th Business Maths Guide Pdf Chapter 10 Operations Research Miscellaneous Problems Text Book Back Questions and Answers, Notes. Tamilnadu Samacheer Kalvi 12th Business Maths Solutions Chapter 10 Operations Research Miscellaneous Problems Question 1. The following table summarizes the supply, demand and cost information for four factors S1, S2, S3, …<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/tnboardsolutions.com\/wp-json\/wp\/v2\/posts\/37749"}],"collection":[{"href":"https:\/\/tnboardsolutions.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/tnboardsolutions.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/tnboardsolutions.com\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/tnboardsolutions.com\/wp-json\/wp\/v2\/comments?post=37749"}],"version-history":[{"count":0,"href":"https:\/\/tnboardsolutions.com\/wp-json\/wp\/v2\/posts\/37749\/revisions"}],"wp:attachment":[{"href":"https:\/\/tnboardsolutions.com\/wp-json\/wp\/v2\/media?parent=37749"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/tnboardsolutions.com\/wp-json\/wp\/v2\/categories?post=37749"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/tnboardsolutions.com\/wp-json\/wp\/v2\/tags?post=37749"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}