# HBC 0212: BUSINESS MATHEMATICS Past Paper

W1-2-60-1-6
JOMO KENYATTA UNIVERSITY
OF
AGRICULTURE AND TECHNOLOGY
University Examinations 2014/2015
SECOND YEAR FIRST SEMESTER EXAMINATION
DATE: AUGUST 2014 TIME: 1½ HOURS
INSTRUCTIONS: ANSWER QUESTION ONE (COMPULSORY) AND ANY OTHER TWO QUESTIONS

Question One (30 Marks)

a) Explain with examples what is:

(i) A set

(ii) A venn diagram

(iii) A universal set

(iv) A Dijoint – set

(v) A Subset

b) (i) Verify that (AUB)1 = A1n B1

(ii) Given that:

U = {3, 4, 5, 6 ………. 12}

A = {3, 4, 8, 9}

B = {4, 5, 7, 9, 10}

C = {3, 4, 5, 6, 8, 9}

D = {4, 6, 8, 11}

Basing on the sets given above, evaluate the following:

(I) C U ( B U ∆)

(II) B n (AUC)

(III) B n φ

(IV) BUB1

c) An ice cream parlour wanted to know what flavours most popular. A survey of 100 customers revealed that 56 customers liked vanilla, 55 customers liked chocolate and 59 customers liked strawberry, 43 customers liked vanilla and chocolate, 41 liked vanilla and strawberry, 40 liked strawberry and chocolate, 30 customers liked all the three of the flavours:

(i) How many customers liked vanilla or chocolate?

(ii) How many customers liked none of these flavours?

(iii) How many customers liked only one flavor?

(iv) How many did not like vanilla?

Question Two (15 Marks)

A company invests in a particular project and it has been estimated that after x months of running, the cumulative profit (¥000) from the project is given by the function 31.5x – 3×2 – 60, where x represent time in months. The project can run for nine months at the most:

a) Draw a graph which represents the profit function.

b) Calculate the ‘break even’ time points for the project.

c) What is the initial cost of the project?

d) Use the graph, to estimate the best time to end the project.

Question Three (15 Marks)

a) A furniture factory manufactures two types of coffee table, A and B. Each table goes through two distinct costing stages, assembly and finishing. The maximum capacity for assembly is 195 hours and for finishing, 165 hours. Each A table requires 4 hours assembly and 3 hours finishing. While B table requires 1 hour for assembly and 2 hours for finishing. Calculate the number of A and B tables to be produced to ensure that the maximum capacity available is utilized.

b) Solve the following system of linear equations:

x, y and z
y: z = 2: 1
10x + y = 0
5x + y + 2z = 15

Question Four (20 Marks)

a ) (i) Differentiate between simple and compound interest.

(ii) A firm plans to invest an amount of money at the beginning of every year in order to accrue a sum of ε100, 000 at the end of five years period. What is the value of the amount, if the investment rate is 14%?

b) (i) What do you understand by the term discounting?

(ii) A departmental store advertises goods at \$700 deposit and three further equal annual payment of \$500. If the discount rate is 7.5%, calculate the present value of the goods.

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