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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:2014
QUESTION ONE – (30 MARKS)
(a) Distinguish between each of the following terms giving an example of each. (i) Singular and non-singular matrix. (4 Marks) (ii) Objective function and decision variables. (2 Marks) (iii) Open and closed input – output model. (4 Marks)
(b) Use matrix method to solve the following set of simultaneous equation 2?? - 2?? = 4 ?? + 5?? = 2 (5 Marks)
(c) Given that a firm has total function given by the equation ? ? 50 1117 3 1 2 3 ? ??? x xxxc and the corresponding revenue function given by ? ? 2 100 x xxR ? ? , determine the profit function and hence find the marginal profit when 20 units of the product are produced and sold. (8 Marks)
2
(d) The following table gives the input output coefficients for a two sectors economy consisting of agriculture and manufacturing
To From Agriculture Manufacturing Agriculture 0.3 0.4 Manufacturing 0.2 0.3
The forecasted final demand for the two sectors are 100 and 50 in agriculture and manufacturing respectively. Determine what gross output of the two sectors will meet this demand. (7 Marks)
QUESTION TWO – (20 MARKS)
(a) A firm has analyzed their operating conditions, prices and costs and have developed the following functions ?????????????? £ ?? = 400?? - 4??2 ???????? £ ?? = ??2 + 10?? + 30 Where ?? is the number of units sold. The firm wishes to maximize profits and wishes to know (i) What quantify 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 ?? = ?? ?? - 2 ?? + 3 and the x-axis. (6 Marks)
(c) Given the curve ?? = ??3 - 2??2 + ?? + 2, find the stationery points on the curve and identify if they are maximum or minimum. (6 Marks)
QUESTION THREE – (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)
3
(d) Given that ? ? ? ? ?
? ? ? ? ? ?
??
?
568 240 141 B . Find
(i) B (4 Marks) (ii) T B (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 (4 Marks)
QUESTION FOUR – (20 MARKS)
(a) Explain three assumptions of linear programming. (6 Marks)
(b) (i) Evaluate dx x x? ? ? ? ? ? ? ? 3 2 46 (3 Marks) (ii) differentiate the function ? ? 3 52 52 x xx y ? ? (5 Marks) (c) Ms. Kawira invested Ksh.50,000 in three ways at 8%, 8.5% and 11% interest in total she received Ksh.4436.25 per year in interest. The interest from 11% investment was Ksh.80,000 more than the interest on the 8% investment. Find the amount she had invested at each rate. (6 Marks)
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