BBM 105: BUSINESS MATHS 1 – Click to view


Answer Question one and any other two Questions.

Question one is compulsory and it carries 30 marks other questions are 20 marks each.

Question one
a) Explain with examples the following set concepts as used in set theory.
i) Universal set ( 2 marks)
ii) Complement of a set ( 2 marks)
iii) Null set ( 2 marks)
iv) Disjoint set ( 2 marks)
v) a sub set ( 2 marks)
b) Consider the following two commodity market model.
Qd1 = 8 – 2P1 + P2
Qs1 = -5 + 3P1
Qd2 = 16 + P1 – P2
Qs2 = -1 + 2P2
Qd1 = Qs1
Qd2 = Qs2
Determine by crammers rule:
i) The value of equilibrium prices (8 marks)
ii) The value of equilibrium quantities

Question two
a) i). Give two examples of a set of numbers that are real numbers. (3 marks)
ii). Define a rational number. (2 marks)
b) There are 1400 students in a school. 1250 can ski, 952 can skate, 60 can neither ski nor skate. How many students can both ski and skate

Question three

Question four

Question five

a) The sales manager of some firm wishes to study the characteristics of the revenue received by the firm. He notices from his study that when price is at 3, the level of output sold is 10, however, when price goes up to 5 then Q = 2. Assume linear relationship between these data and determine;
i) Demand function ( 5 marks)
ii) TR function ( 3 marks)
iii) AR function ( 3 marks)
iv) MR function ( 2 marks)
v) Comment on your results in (i) and (iii) above ( 2 marks)
b) Find the partial derivatives of the following function

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