QTS0103 BUSINESS MATHEMATICS
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BUSINESS MATHEMATICS (QTS0103)
CONTINUOUS ASSESSMENT 1
INDIVIDUAL ASSIGNMENT (30%)
Question 1 (10 marks)
|
(a) |
Solve the following equations. Give your answer to 3 decimal places.
(i) (ii) 2y2 − 4y = y 2 + 8 |
[2 marks] [2 marks] |
(b) Solve the following inequalities:
(i) −12 < 5x + 1 < 3 [2 marks]
(ii) 5x2 + 2x − 3 ≤ 0 [2 marks]
(iii) |2y + 5| > 3 [2 marks]
(Total 10 marks)
Question 2 (10 marks)
(a) The function f and g are given by f(x) = 2x2 − 1 and g(x) = 3x3 .
(i) Find the value off(3). Give your answer to 3 decimal places. [1 mark]
(ii) Determine the domain of g(x) [1 mark]
(iii) Find f ∘ g (x). [1 mark]
(iv) Find the value of g ∘ f(0). [1 mark]
(b) Find an equation of the line that passes through the point (2, −1) and is perpendicular to the line that passes through the points (1, 4) and (2, 2). [3 marks]
(c) Find the points of intersection(s) of the lines of the functions f(x) = 2x2 + 2 and
g(x) = 3x2 + x − 1 . Provide your answers to one decimal place. [3 marks]
(Total 10 marks)
Question 3 (10 marks)
(a) Your firm manufactures chairs at $20 per unit and sells at a price of $50 per unit. Given the fixed cost for the company is $30,000. Find the breakeven quantity and revenue. [3 marks]
(b) The weekly demand and supply functions for a product given by p = −0.2x# + 30 and p = 4x# + 3x − 70 respectively, where p is the unit price in dollars and x is the quantity demanded in units of a hundred.
(i) Determine the quantity supplied when the unit price is set at $50. [2 marks]
(ii) Determine the equilibrium price and quantity. [2 marks]
(c) Your firm manufactures SD cards at a cost of $3 per unit, fixed cost of $50,000 and sells it at a price of $6 per unit.
(i) Determine the firm’s profit function. [2 marks]
(ii) Calculate the firm’s profit/loss if it sells 15,000 units. [1 mark]
(Total 10 marks)
2023-07-28