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Hbc2111:Management Mathematics Question Paper
Hbc2111:Management Mathematics
Course:Bachelor Of Commerce
Institution: Meru University Of Science And Technology question papers
Exam Year:2013
QUESTION ONE - (30 MARKS)
a) Evaluate ; i. 62 + 4 3
(3 Marks) ii. lim1{2 1} (5 Marks) b) Given that the total function for a blender is = 36 0.012 , where is the number of units sold. What is the average rate of change in revenue () as increases from 10 to 20 units? (4 Marks) c) An economy consist of a wood product industry and mineral industry. To produce one unit of wood requires 0.12 units of its own output and 0.09 units of mineral industry output. To produce one unit of mineral requires 0.11 units of its own output and 0.15 units of wood industry. If sulphises of 1738 units of wood and 1332 units of mineral are desired. Find the gross production of each industry. (5 Marks) d) Solve by matrix method + 2 = 3 3 + = 4 2 + = 2 e) i) Define the following terms as used in Markov Processes. (i) Transition matrix (ii) Steady state matrix (4 Marks) ii) Because of the continued successful implementation of an urban renewal program. It is expected that each year 3% of the population currently residing in the city will move to the
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suburbs and 6% of the currently residing in the suburbs will move into the city. A present 65% of the total population of the metropolitan area lives in the city itself while the remaining 35% lives in the suburbs. Assuming that the total population of the metropolitan area remains constant. What will be the distribution of the population two years from now? (5 Marks)
QUESTION TWO (20 MARKS)
a) A firm has analysed their operating conditions, prices and costs and have developed the following function; £ = 400 42 £ = 2 + 10 + 30 Where q is the number of units sold. The firm wishes to maximize profits and wishes to know; i. What quantity should be sold and at what price. (5 Marks) ii. What will be the amount of profit? (3 Marks) b) Find the area enclosed by the curve = 1 + 3 and the x-axis. (6 Marks) c) Given the curve = 3 22 + + 2, find the stationery points on the curve and identify if they are maximum and minimum. (6 Marks)
QUESTION THREE (20 MARKS)
a) A manufacturer is to make a new fertilizer which is to be a mixture of two ingredients A and B. the properties of the two ingredients are Bone meal Nitrogen Lime Phosphate Cost/kg Ingredient A 20% 30% 40% 10% 1L Ingredient B 40% 10% 45% 5% 8 It has been decided that; i. The fertilizer will be sold in bags of 100kg ii. It must contain at least 15% nitrogen iii. It must contain at least 8% phosphate iv. It must contain at least 25% bone meal
The manufacturer wishes to meet the above requirements at minimum cost;
i. Formulate the problem a s a linear programming problem. (6 Marks) ii. Determine the quantities of ingredients A and B that must be produced. (5 Marks) iii. Determine the minimum possible cost. (2 Marks)
b) Evaluate i. 2 2 0
(2 Marks) ii. ( + ) 2 0 3 2 (4 Marks)
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QUESTION FOUR (20 MARKS)
a) State two assumptions of open input-output model. (2 Marks) b) Highlight four significance of mathematics to business decision making. (4 Marks) c) Given the marginal profit function of a firm as = 200 4 where x is the sales in units. If the firm breakeven on sales of 10 units, find the fixed cost of the firm. (4 Marks) d) Given that;
=
2 4 1 0 4 2 8 6 5 Find i. (4 Marks) ii. (2 Marks) e) Using a graph, find the feasible region and the maximum value of 5 + 11 subject to the following constraints. 5 + 2 54 2 + 4 60 0, 0
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