Business Mathematics — DU B.Com (P) Previous Year Question Papers

1. (a) The following matrix gives the proportionate mix ofconstituents used for three fertilizers : (i) If sales are 1000 tins (of one kilogram) per week, 20% being fertilizer X, 500/o being fertilizer Y and 30% being fertilizer Z, how much of each constituent is used. (fi) If the cost of each constituent is 60 paise, 70 paise, 80 paise and 100 paise per 100 grams respectively, how much does 1 kg tin of each fertilizer costs? (iii) What is the total cost per week? (6) Mr. X has invested {35000, that he had divided into three investments. Part of the money is invested in a savings account with an annual return of 60/o, partly in 7°/o annual yield bonds and the remainder in business. In 2015, when he lost 6% of the money that he invested in the business, his net income from all the three investments is €660. If he invested €3000 more in the business than in the savings account, how much was invested in each. Use matrix algebra. (6) a) An economy consists of sectors- manufacturing and agriculture. To produce one unit of manufacturing output, 0.1 unit of manufacturing goods and 0.01 unit of agriculture goods are required as input. One unit of agriculture output requires 40 units of manufacturing goods and nil units of agricultural goods as inputs. A unit of manufacturing goods requires 4 man-hours of labour and a unit of agriculture requires 100 man~hours of labour. Calculate the total labour requirement if 501akh units of manufacturing goods and 21akh units of agriculture goods are used for final consumption. Supposing the wage rate is {10 per man hour, calculate the equilibrium prices of manufacturing and agrioultural goods. (6) A holding company H has two subsidiaries A and 8. The subsidiaries own a small portion of the share capital of H. The proportionate ownership of the group is given below : Owner of Shares Proportion of share capital held in company Outside Shareholder 0,90 0.30 0.10 If the separately earned profits of H, A and 8 are {3,00,000, €1,50,000 and €1,00,000 respectively, find the total profits (i.e. separately earned profit plus share in the profits of other companies) of each company by using matrix algebra. Also verify that the sum of profits allocated to outside shareholders equals the sum of the separately earned profits of all the companies. (6) 2. (a) The production function for a commodity is : Q = 10L -0.1L2 + 15K - 0.2K2 + 2KL where L is Labour, K is Capital and Q is production. (i) Calculate the marginal products of the two inputs 10 units each of labour and capital are used. (ii) If 10 units of capital are used, what is the upper limit for use of labour which a rational producer will never exceed? (6) The joint cost function of a firm producing two products is given by where x and y denote their units. (i) Find the value of x and y that minimize C (x, y) (ii) Compute the minimum cost. (6)