Business Mathematics Question Paper
Business Mathematics
Course:Bachelor In Business Management
Institution: Moi University question papers
Exam Year:2014
Answer question ONE and any other THREE questions
QUESTION ONE
a) Discuss the areas of application of business mathematics to a manager (5 marks)
b) Highlight four assumptions of markov process (4 marks)
c) If A={m,n,o,p} B={m,o,p,q} C={m,p,r} and the universal set is defined as U={k,l,m,n,o,p,q,r,s,t} then what is:
i)AUB ii) AUC iii) BnC iv) (AUB)’ v) (AnC)’ (4 marks)
d) Given the following demand function; Q=(40- 2P)/3 ; where Q is the level of output and P, the price per unit. The cost function is defined as TC= 0.5Q2 + 10Q-225.
i. Derive the revenue function and the cost function.
ii. Calculate the corresponding break-even point. (6 marks)
e) A firm has an advertising budget of shs 720 000. It wishes to allocate this budget to two media: magazines and televisions, so that total exposure is maximized. Each page of magazine advertisement is estimated to result in 60 000 exposures, whereas each spot in television is estimated to result 120 000 exposures. Each page of magazine advertisement costs shs 9000 and each spot in television advertising costs shs 12 000. Formulate the linear programming problem (6 marks)
QUESTION TWO
a. Explain the importance of break-even analysis in a small business. (6 marks)
b. You are given consumption function: C= 120+ 0.75Yd where Yd is disposable income. You are also given the following information: Yd= Y-T and that T= tY. Where Y is total income; T, total tax; and t, tax rate.
i. Express consumption C, as a function of total income, Y.
ii. Find the level of C, if t=0.3 and Y= 5000 (9 marks)
QUESTION THREE
a) Discuss the application functions in business (6 marks)
b) Solve the following set of functions using matrix algebra inverse method
X1 + 3X2 + 3X3 = 37
X1 + 4X2 + 3X3 = 47
X1 + 3X2 + 4X3 = 50 (9 marks)
QUESTION FOUR
a) Using examples demonstrate the meaning of the following concepts
i. Union of sets (2 marks)
ii. Intersection of set (2 marks)
iii. Compliment of a set (2 marks)
iv. A disjoint (2 marks)
b) A music shop specializes in organs and various other keyboard machines. Many modern machines have MIDI, and any machine can either be portable or fixed. The shop also stocks second hand machines. Part of the managers quarterly report, reflecting the stock position, reads: “Currently, 62 machines are in stock of which 16 are second hand. New portable machines in total, 28 having MIDI. We currently have no fixed, second hand MIDIs or non-MIDI, second-hand portables.
i. Have MIDI?
ii. Are new portables?
iii. That are new and fixed, do not have MIDI?
iv. Are second hand, portable MIDIs? (7 marks)
QUESTION FIVE
a) Highlight four management applications of linear programming
b) A factory produces two products X and Y each of which must pass through two production processes A and B. Product X requires 10 hours in A and 8 in B, while product Y requires 10 hours in A and 3 in B. the maximum capacity of process A for a certain period is 1200hours and due to the cost and manpower agreements, process B must be used at least 4800hours over the same period. Due to fixed commitments, at least 600 Y products must be produced, while a maximum of 500 X products will be produced over the given period.
i. Formulate the constraints for the above problem
ii. If X has a contribution of Kshs. 100 and Y Kshs. 140, find the points that maximize and minimize total contribution and give the value of these contributions.
(11 marks)
QUESTION SIX
a) Outline four applications of transition matrix in business (4 marks)
b) A bank classified its customers as loyal, switchers or split, depending on the numbers of orders placed in a year. Records indicate there are 200 customers who are classified as loyal and 200 also classified as switchers and 200 split: furthermore each year 10 of the loyal customers are re-classified as swiitchers and 24 split; 10 of the switchers customers are re-classified as loyal and 10 as split; and 18 of the split customers are re-classified as loyal and 20 as switchers.
Determine:
i. The transition matrix.
The percentage of customers that the company expect to have in each category in the long-run
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