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Business Mathematics – Suggested Answer and Marking Scheme

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					                        DIPLOMA IN
     ACCOUNTING / BUSINESS ADMINISTRATION / MARKETING



                    MAY 2008 EXAMINATION


                   BUSINESS MATHEMATICS

                       Paper No : 3MSC0104

                   TIME ALLOWED : 3 HOURS



INSTRUCTIONS TO CANDIDATE:

1.    Answer all questions in SECTION A.
2.    Answer any FOUR (4) questions out of FIVE (5) questions in
      SECTION B.




                                1
                                        SECTION A
                            (Answer all multiple choice questions)


A1.   Solve the simultaneous equations.

       y  4  2x
       2
       y  4x  0

                 x  1               x  4
      (a)                     or     
                 y  2                y  4
                 x  3               x  1
      (b)                     or     
                 y  2               y  3
                 x  2               x  3
      (c)                     or     
                 y  0                y  3
                 x  1               x  2
      (d)                     or     
                  y  1              y  2


A2.   RM 7000 compounded at 7% becomes RM 9792 after n years. What is n?

      (a)    4
      (b)    6
      (c)    5
      (d)    7


A3.   What is the future value of RM 5400 in 5 years time, when it is locked in a FD that
      yields 4% p.a.?

      (a)    RM 6570
      (b)    RM 2100
      (c)    RM 1050
      (d)    RM 8010


A4.   RM 7800 is compounded at 4.52% p.a. for 5 years. What is the return at the end of the
      tenure?

      (a)    RM 9161.40
      (b)    RM 8400
      (c)    RM 9729.52
      (d)    RM 10005.40




                                                 2
A5.   When 1000 units are produced, the Average Revenue is RM 3.50 whilst the Average
      Cost is RM 2.30. What is the Average Profit?

      (a)     RM 1.00
      (b)     RM 5.80
      (c)     RM 3.00
      (d)     RM 1.20


A6.   If the Total Cost is given as x 4  14x3  22x 2  18x  10 , what is Average Cost?

      (a)     4 x 3  42x 2  44x  18
      (b)     4 x 2  44 x
      (c)     x 5  x 3  22 x
      (d)     x3  14x 2  22x  18  10x 1


A7.   If Total Revenue is given as 14x  7 x 2 , what is the Marginal Revenue?

      (a)     14  14x
      (b)     14  x 2
      (c)     14x  7 x  C
      (d)     14x  C


A8.   Evaluate:
      1

       x  4x  dx
      0
                       1
                       2




                  41
      (a)     
                  12
      (b)     0
                  14
      (c)     
                   3
      (d)     1


A9.   Differentiate the following: y  9 x 5  6 x 3  3x 2

      (a)     45x 4  18x 2  6 x
      (b)     45x 4  18x 2  6 x  C
      (c)     9 x 6  6 x 4  3x 3
      (d)     8x




                                                 3
A10.   Integrate the following:


                 2
               x  3 dx

                  x2        3
       (a)             4x 2  9x  C
                   2
                  x2        1
       (b)             6x 2  9x  C
                   2
       (c)        3x 2  9 x  C

       (d)        4 x 2  5x

                                                                        (Total : 20 marks)




                                      SECTION B
                 (Answer any FOUR (4) questions out of FIVE (5) questions)


Question 2

(a)    If RM 900 is invested at 7.2% p.a., how long will it take for the money to amount to
       RM 2700?

                                                                                 (3marks)

(b)    An investment of RM 81,000 was made at a simple interest rate of 9% per annum.
       (ii)      Find the accumulated sum after 6 years.
                                                                                 (3marks)
       (iii)     Find the total interest earned.
                                                                                  (1mark)

(c)    Find the effective rate interest of:

       (i)       10 % pa compounded monthly
       (ii)      1.2 % per month
                                                                                 (4marks)




                                                   4
(d)   Given Matrices:
           2 0
           1 2
      A      
              
      
           1 0
            2 8
      B        
                
          3 5
      C  
           1 7 
                
      
              
      Find:
              3
      (i)       A                                            (1 mark)
              2
      (ii)    4C – B                                         (2 mark)
      (iii)   AB+C                                           (3 marks)


              2 2
(e)           3 0  , what is Q  AB ?
      If Q       
                                2

                  
                                                              (3 marks)
                                                      (Total : 20 marks)



Question 3

(a)   Find the derivative of the following:
      (i)     y  16 x 4  7 x 3  5 x 2  12 x              (2 marks)
                                     2 2
      (ii)    y  4 x 3 x            x                     (3 marks)
                                     3
                    3 3 2 6 1 7
      (iii)   y      x  x  x                              (3 marks)
                    4    5   3


(b)   Find the integral of the following:

               7 x                       
                            4 x 2  2 x  5 dx
                       3
      (iv)                                                   (3 marks)

                x4  x3  x2
      (v)           x2
                             dx                              (2 marks)




                                                  5
(c)   Find the x value for the turning points of the following function:
       y  6 x3  8x                                                               (3 marks)


(d)   Find the x values for the turning points of the following function:
       y  4 x 3  3x 2  7                                                         (4 marks)
                                                                            (Total : 20 marks)



Question 4

(a)   A manufacturer is producing a certain type of DVD players. The total cost (RM) of
      producing x DVD’s per week is given as 900x + 2000. Given that the demand
      function, p = 700 – 2x (p represents price and x represents quantity demand),
      determine the profit function.
                                                                                    (3 marks)


(b)   The demand curve for a commodity is x = 60 – 4p (p represents price and x represents
      quantity demanded).

      (i)      Find the quantity demanded if the price is 9.                        (1 mark)

      (ii)     What quantity would be the quantity that is demanded if the commodity is free?
                                                                                 (1 mark)

      (iii)    Express the demand function in terms of p.                           (2 marks)




(c)   The supply curve of a commodity is p  15  5x (p represents price and x represents
      quantity demanded)
      (i)      Find the price of the quantity supplied is 1.                        (1 mark)

      (ii)     Find the quantity supplied if the price is 70.                       (1 mark)

      (iii)    Express the supply function in terms of x.                           (2 marks)




                                                6
(d)    A manufacturer sells his product at RM 9 per unit. Fixed costs are constant at RM
       4000 regardless of the number of units of products involved. The variable costs are
       estimated at 30% of total revenue.

       (i)     What is the equation of the revenue function?                         (1 mark)

       (ii)    What is the total revenue for the sale of 7200 units of product?       (2 marks)

       (iii)   What is the total cost when 7200 units of product are sold?           (4 marks)

       (iv)    What is the quantity at which the manufacturer will cover its fixed costs?
                                                                                    (2 marks)
                                                                           (Total : 20 marks)



Question 5

The marginal cost and the marginal revenue functions for a company are as follows:
MC  x 2  10 x  68

MR  70  3x

Where x units is the output level or quantity.

(a)    Find the total revenue functions for the company.                            (2 marks)

(b)    If it is known that the fixed cost is RM 18, what would the total cost function be?
                                                                                    (2 marks)

(c)    Find the profit function.                                                    (2 marks)

(d)    Determine the output at which the profit will be maximized.                  (6 marks)

(e)    Establish the number of units of output at which TR will be maximized.       (2 marks)

(f)    What is the:

       (i)     Price at this output level?                                          (2 marks)
       (ii)    Point of elasticity at this output level?                            (4 marks)


                                                              p  dx 
       (Point of elasticity of demand (E) is defined as E       
                                                              x  dp 
                                                                 
                                                                             (Total : 20 marks)




                                                 7
 Question 6

 A manufacturer can produce two types of candy, P and Q, using the same equipment in a
 similar 3 stage process involving mixing, cooking and packaging. Boxes of P sell at a profit
 of RM 4 and boxes of Q sell at a profit of RM 5. For each production run, the processing time
 per box and the availability of the equipment are as follows:


                              Processing times per box (minutes)

                                Candy       Candy       Equipment Availability
                                  P           Q

                   Mixing          4           8               48 hours
                   Cooking        20          16              120 hours
                  Packaging        6           2               30 hours


 The manufacturer’s objective is to maximize profit:

 You are required to:

(a)     State the objective function and constraints.                              (6 marks)

(b)     Graph the constraints, shading the feasible region.                       (10 marks)

(c)     Recommend a suitable product mix for the manufacturer                      (3 marks)

(d)     Calculate the maximum profit.                                               (1 marks)
                                                                            (Total : 20 marks




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