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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:2012
QUESTION ONE (30 MARKS)
a) Solve the following system of equation using matrix algebra. 21 + 2 3 = 11 1 22 + 22 = 2 31 2 + 32 = 5 (6 Marks) b) A company estimates that the demand for its product is function of the price it charges. The demand function is = 280,000 400, where q is the number of units demanded and p is the price in Kenya shillings. The total cost of producing of units of the product is estimated by the function = 350,000 + 300 + 0.0012. determine i. The number of units produced in order to maximize annual profit. (6 Marks) ii. The price to be charged. (1 Mark) iii. The annual profit expected. (3 Marks) c) A company produces two types of hats. Every hat A requires twice as much labour time as the second hat B. If the company produces only hat B then it can produce a total of 500 hats a day. The market limits daily sales of the hat A and hat B to 150 and 250 hats. The profits on hat A and B are Ksh.8 and Ksh.5 respectively. Solve graphically to get the optimal solution. (8 Marks) d) Differentiate = 54 + 4 1 22 + 1 3 with respect to x. (3 Marks) e) Discuss the properties that must exist for a transition matrix to be considered a Markov process. (3 Marks)
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QUESTION TWO (20 MARKS)
a) Find from the first principle () of the function = 23.(6 Marks) b) Explain five advantages of using linear programming in decision making. (5 Marks) c) The marginal cost for a company’s product s C -2Q-Q2 and the marginal revenue function is MR=25-5Q-2Q2 where Q is the level of output. Calculate; i. The output that maximizes profit. ii. The total profit and the output that maximizes profit. (9 Marks)
QUESTION THREE (20 MARKS)
a) Determine the inverse of the following matrix
=
3 1 0 1 2 2 5 0 1 (8 Marks) b) A researcher method to consider part of anatoual input-output model. She restricted her4self to two industries and had the following information; input output coefficients, A is
=
1 8
1 3
1 2
1 6
The output of each industry to final demand is given
= 1001 3407
Using input output analysis, calculate the output of each of the two industries. (8 Marks)
c) Highlight the limitations of linear programming in decision making. (4 Marks)
QUESTION FOUR (20 MARKS)
a) A manufacturing firm has developed a transition matrix containing the times that a particular machine will operate or break down in the following, given its operating condition in the present week. 0.4 0.8 0.6 0.2 i. If the machine operated in week 1, find the probabilities that the machine was operate or break in week 3. (5 Marks) ii. Algebraically determine the steady stable probabilities for this transition matrix. (5 Marks)
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b) Evaluate (2 + 2 2 1 3 0
) (6 Marks) c) Describe the characteristics of linear programming problems. (4 Marks)
QUESTION FIVE (20 MARKS)
a) The marginal cost function of producing q units of a product is given by MC=25+0.05q and the marginal revenue is given by MR=75-0.016q. i. Find the total cost function and the total revenue function if the fixed cost is 40,000 shillings and fixed is 0 ii. Determine the profit maximizing level of output. (8 Marks) b) Differentiate with respect to x the function. = 32 + 4 1 (6 Marks) c) Solve using matrices 2 + 6 = 6 7 + 8 = 5 (6 Marks)
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