代写QTS0103 Business Mathematics Continuous Assessment 1代写数据结构语言程序

BUSINESS MATHEMATICS (QTS0103)

CONTINUOUS ASSESSMENT 1

INDIVIDUAL ASSIGNMENT (30%)

Question 1 (10 marks)

(a)       Solve the following equation. Give your answer to 2 decimal places (if applicable).

x+5/2x = x/1                                                                                                           [2 marks]

(b)       Solve the following inequalities:

(i)        2x2 + 3x + 1 ≤ 1                                                                                             [2 marks]

(ii)        |3x + 5| ≤ 2                                                                                                    [2 marks]

(c)       Given: f(x) = 2/x and g(x) = x2 − 2x + 1

(i)        Determine the domain of g(x)                                                                 [1 mark]

(ii)       Find the function: g(0)                                                                                       [1 mark]

(iii)      Find the function: fog(2)                                                                            [2 marks]

(Total 10 marks)

Question 2 (10 marks)

(a)       Find an equation of the line that passes through the point (5, −2) and is perpendicular to the line that passes through the points (1, 4) and (2, 2).         [3 marks]

(b)       NX Tech Ltd had sales of $5 million in its first year of operation. If the sales increase by 20% per year thereafter, determine the company’s sales in the tenth year and its total sales over the fifteen years of operation. Give your answers to the nearest dollar.

(c)       Find the points of intersection(s) of the lines of the functions f(x) = 2x2  + 4x + 6 and g(x) = 6x2  + 6x   [3 marks]

(Total 10 marks)

Question 3 (10 marks)

(a)       Bright Lights Ltd  manufactures table lamps at $5 per unit and sells at a price of $20 per unit.  Given  the  fixed  cost  for  the  company  is  $60,000,    calculate  the  firm’s breakeven quantity and breakeven revenue.  [3 marks]

(b)       The  demand and  supply functions for a product given by p = −2x2  + 50  and p = 3x2  + x − 200 respectively, where p is the unit price in dollars and x is the quantity demanded in units of thousand.

(i)        Determine the quantity supplied when the unit price is set at $100. Round your answer to the nearest unit. [2 marks]

(ii)       Determine the equilibrium price and quantity. Give your workings and answer to four decimal places. [2 marks]

(c)       A firm manufactures card games at a cost of $2 per unit and sells it at $5 per unit. The fixed cost for the firm is $30,000.

(i)        Determine the firm’s profit function.                                                      [2 marks]

(ii)       Calculate determine how many units the firm has to sell to profit $30,000.   [1 mark]

(Total 10 marks)