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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:2011
QUESTION ONE
a) (i) Using an appropriate illustration, discuss the significance of matrices in business management. (3 Marks) (ii) Let A= , B= and C=
Show that A(B+ C) = AB + AC (4 Marks)
b) Differentiate with respect to X the function (i) y=2(3x +4)4 (4 Marks) (ii) Evaluate -2x)dx (2 Marks)
c) Given that the total revenue function for a blender is R(x) = 36x-0.01x2 where x is the number of units sold. What is the average rate of change in revenue R(x) as x increases from 10 to 20 units. (4 Marks)
d) The marginal cost function for a month for a certain product is MC=3X + 50 and the fixed cost is Ksh100 per month. Find the total cost function for the month. (3 Marks) e) A two segment economy consists of manufacturing and Agriculture. To produce one unit of manufacturing output requires 0.40 units of its own output and 0.20 units of Agricultural output. To produce one unit of Agricultural products requires 0.30 units of its own output and 0.40 units of manufacturing output. If there is a demand of 240 units
of manufacturing and 90 units f Agriculture, what should be the output of each segment? (5 Marks)
f) Using a graph, find the feasible region and the maximum value of 5x +11y subject to the following constraints. 5x + 2y 2x + 4y x (5 Marks)
QUESTION TWO (20 MARKS) a) State and explain briefly four assumptions of linear programming (8 Marks) b) Maxwell limited, as a result of past experience and estimates for the future, has decided that the cost of production of the sale product, E, on an advanced process machine is C=1064 + 5E + 0.04E2 and sold. The marketing department has estimated that the price of the product is related to the quantity produced and sold by the equation. P=157 – 3E E= quantity sold. Required: (i) Determine the price and quantity that will maximize profits. (4 Marks) (ii) Determine the price and quantity that will maximize revenue (4 Marks) (iii) Differentiate with respect to X, the function (4 Marks)
QUESTION THREE (20 MARKS)
a) The revenue function for a product is given by R(x) =10x + where x is the number of units sold and R is in Kenyan shillings. (i) Find the marginal revenue function (5 Marks) (ii) Find the marginal revenue when 15 products are sold (1 Mark) b) Use the inverse matrix method to solve the following system of equations -x+z =1 X + 4y -3z=-3 x-2y + z = 3 (10 Marks)
c) The weekly sales S of a product during an advertising campaign is given by S= , 0
Where t is the number of weeks since the beginning of the campaign and S is in thousands of shillings. Determine the maximum weekly sales after the end of the campaign period (4 Marks)
QUESTION FOUR (20 MARKS) a) A manufacturer is to market a new fertilizer which is to be a mixture of two ingredients A and B. The properties of the two ingredients are: Ingredient Analysis Bone meal Nitrogen Lime Phosphate Cost /kg Ingredient A 20% 30% 40% 10% 12 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, atleast 15% nitrogen (iii) It must contain atleast 8% phosphates (iv) It must contain at least 25% bone meal. The manufacturer wishes to meet the above requirements at a minimum possible cost. (i) Find the quantities of products A and B that must be produced. (ii) Determine the minimum possible cost (10 Marks)
b) Given that =(2 Find the derivative of f(x) and simplify your answer completely (3 marks)
c) Given that the marginal cost for a certain product is represented by the equation Mc= and the fixed cost for the month is Ksh11,125. Determine the total cost for producing 300 items per month. (4 Marks)
d) Find the integral given below x)dx (3 Marks)
QUESTION FIVE (20 MARKS)
a) Given that the marginal profit function of a product is
y=200-4x where y is in Ksh and x is the sales in units. If the firm breakevens on sales of 10 units. Calculate the fixed costs of the firm. (4 Marks) b) If y=4x3-6x2-7x+2 Find (3 Marks)
c) Obtain the turning point of the function. f(x) =2x3-3x3-12x-7 and use the 2nd derivative test to classify them (6 Marks)
d) A theatre charges 4 dollars for children and 8 dollars for adults. One weekend 1000 people attended the theatre and the admission receipts totaled 6260 dollars. These can be represented by the system where x is the number of children and y is the number of adults
attending . Find the number of children and the number of adults who attended. (3 Marks)
e) Find from the first principle the derivative of the function f(x) = 2x3 (4 Marks)
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