BBE/B-COM MATHSAssignment APPLICATION of MATRICES One secret of success in life is for a man to be ready for his opportunity when it comes. STEP TO SUCCESS TUTORIALS PH:9654587567 Q1 An automobile dealer sells two car models, standard and deluxe. Each is available in one of the two . colours, white and red. His sakes for the month of January and February are given by the matrices. Standard 2 A= 3 Deluxe 1 4 3 B= 2 1 3 Find the total sales for each model and color for both models. Q2 The sales figure for two dealers during January showed that dealer A sold 5 deluxe, 3 premium and 4 . standard cars, while dealer B sold 7 deluxe, 2 premium and 3 standard cars. Total sales over the two month period of January – February revealed that dealer A sold 8 deluxe, 7 premium and 6 standard cars. In the same 2 – month period, dealer B sold 10 deluxe, 5 – premium and 7 standard cars. Write 2 X 3 matrices summarizing sale data for January and the other 2 – month period for each dealer. Hence find the sales in February for each dealer. Q3 There are two Families A and B, there are 4 men, 6 women and 2 children in Family A, and 2 men, 2 . women and 4 children in Family B. The recommended daily allowance for calories is: Man: 2400, Woman:1900, child:1800 and for proteins is Man:55gm, Woman:45gm, Child:33gm. Represent the above information by matrices. Using matrix multiplication, calculate the total requirements of calories and proteins for each of the two families. Q4 A student has 4 places where he can eat lunch. The college canteen charges Rs.8 for a Dosa, Rs.3 for . French fries and Rs.5 for a soft drink. The campus coffee house charges Rs.10 for a Dosa, Rs.2 for French Fries and Rs.4.50 for a soft drink. A fast food place charges Rs.8 for a Dosa, Rs.4 for a French fries and Rs.5 for a soft drink. A nearby restaurant serves Dosa for Rs.12, French Fries for Rs.5 and a free soft drink for any order. Express the above information in a 4 X 3 matrix. The student wishes to buy 1 dosa, 2 orders of French fries and a soft drink. Find, using matrix algebra, the cost of lunch at each place. Assuming that the student has no preference for any of the places, decide where he should eat to spend the least amount of money. Q5 A firm produces three products A, B and C which it sells in two markets. Annual sales in units are given . as follows. Market: A I II 8000 7000 Units Sold B 4000 18000 C 16000 9000 If the prices per unit of A, B and C are Rs.2.50, Rs.1.25 and Rs.1.50 respectively and the costs per unit are Rs.1.70, Rs.1.20 and Re.0.80 respectively, find the total profit in each market by using matrix algebra. Q6 In a certain city there are 50 colleges and 400 schools. Each school and college has 18 peons, 5 clerks and . 1 cashier. Each college in addition has 1 section officer and 1 librarian. The monthly salary of each of them is as follows. Peon – Rs.300, Clerk – Rs.500, Cashier – Rs.600, Section officer – Rs.700 and Librarian – Rs.900. Using matrix notation, find (a) total numbers of posts of each kind in schools and colleges taken together. (b) the total monthly salary bill of all the schools and colleges taken together. Q7 A firm produces three products P1, P2 and P3 requiring the mix – up of three materials M1. M2 and M3. . The per unit requirement of each product for each material is as follows: M1 M2 M3 A = ,Using matrix notation, find 2 4 2 3 2 4 1 5 2 (i) the total requirement of each of the material if the firm produces 100 units of each product. (ii) the per unit cost of production of each product if the per unit costs of materials M1, M2 and M3 are Rs.5, Rs.10 and Rs.5 respectively, and (iii) the total costs of production if the firm produces 200 units of each product. Q8 Three firms A, B and C supplied 40, 35 and 25 truck loads of stones and 10, 5, 8 truck loads of sand . respectively to a contractor. If the costs of stone and sand are Rs.1,200 and Rs.500 per truck load respectively, find the total amount paid by the contractor to each of these firms, by using matrix method. Q9 A firm has two machines M1 and M2 costing Rs.45,000 and Rs.30,000. Each has 5 years life with scrap . value nil. Find the depreciation of each machine for each year using matrix notation if (a) both are depreciated by sum of the years digit method, (b) first is depreciated by sum of the year’s digit method and second by the straight line method. Q1 A baker makes bread, sweet patties and biscuits. He requires flour, egg, sugar, milk and yeast for his 0. preparations. The requirements of these basic items for making the bread, sweet patty and biscuits is as follows: Bread Flour Egg Sugar Milk Yeast 250gm 0 125gm 0.05l ¼ cake Sweet Patty 50gm ½ 100gm 0.02l 1/8cake Biscuits 8gm ¼ 25gm 0.01L 0 The baker buys the flour for Rs. 2.20 per kg and sugar for Rs.2.40 per kg at controlled prices. An egg costs him Re.0.25, a litre of milk Rs.1.80 and a cake of yeast Re.0.80.What is the cost of making a bread, a sweet patty and a biscuit? Use matrix system. Q1 A firm produces chairs, tables and cupboards, each requiring three types of raw material – timber, nails and varnish. 1. You are given below, the units of different raw materials required for producing one unit of each product: Product Chair Table Cupboard Timber(c.ft) 0.7 1 3.2 Nails(dozen) 2 4 6 Varnish(Litres) 1 1.5 2 If the firm produces 300 units of each product, find the quantity of each raw material using matrix algebra. Q1 An amount of Rs.5,000 is put into three investments at the rates of interest of 6%, 7% and 8% per annum 2. respectively. The total annual income is Rs.358. If the combined income from the first two investment is Rs.70 more than the income from the third, find the amount of each investment by using matrix algebra. Q1 Mr. X invested a part of his investment in 10% bond A and a part in 15% bond B. His interest income 3. during first year is Rs.4,000. If he invests 20% more in 10% bond A and 10% more in 15% bond B, his income during the second year increases by Rs.500. Find his initial investment and the new investment in bonds A and B using matrix method. Q1 A firm produces two products P1 and P2 passing through two machines M1 and M2 before completion. 4. M1 can produce either 10 units of P1 or 15 units of P2 per hour. M2 can produce 15 units of either product per hour. Find daily production of P1 and P2 if time available is 12 hours on machine M1 and 10 hours on M2 per day using matrix inversion. Q1 Food I has 3 units of vitamin A, 9 units of vitamin B and 12 units of vitamin C. Food II has 6, 9 and 15 5. units respectively and Food III has 9, 0, 9 units respectively. 33 units of vitamin A, 27 units of B and 60 units of C are required. Find the amount of three foods that will provide exactly these amounts. Use matrix method. ANSWERS Ans 1. Ans 2. Ans 3. 5 5 2 7 3 4 2 3 3 4 24600 556 15800 332 Ans 4. Rs.19 Rs.18.50 Rs.21 Rs.22 17800 12800 (a) 8100 2250 450 50 50 (i) (b)Rs3905000 Ans 5. Ans 6. Ans 7. [ 800 (ii) 45 65 60 900 800] (iii)Rs.34,000 Ans 8. Ans 9. A – Rs53,000 (a) 15000 12000 9000 6000 3000 10000 8000 6000 4000 2000 (b) 15000 12000 9000 6000 3000 6000 6000 6000 6000 6000 Ans 10. B – Rs44,500 C –Rs34,000 1.14 0.611 0.1581 [1470 3600 1350] Ans 11. Ans 12. Ans 13. Ans 14. Ans 15. 1000, 2200 and 1800 Initial=10000Rs and Rs20000 in Bond A and Bond B. New investment =Rs.12000 and Rs.22000 60 and 90