a) Given the cost function

Required:
i) Evaluate C(+2) ,                                                                                         (2.5 marks)

ii) Evaluate C(-2) .                                                                                         (2.5 marks)

b) Evaluate each of the following for the given value:

c) A paper producing company has determined that its profit from selling x hundred boxes of envelopes is given by the expression:

Required:
i) Determine the number of boxes the company must sell to break even.                                                                          (5 marks)

ii) Determine the number of boxes the company must sell to make money.                                                                      (5 marks)

The personnel department of Dropper Ltd, a large cocoa processing company in DropperLand, is concerned about absenteeism among its shop floor workforce. There is a general feeling that the underlying trend has been rising, but nobody has yet analysed the figures. The total number of shops employees has remained virtually unchanged over the few years.
The mean number of absentees per day for each quarter of the years 1999 to 2001 and quarter 1 in 2002 is given in the table below:

Required:
a) Plot the data on a graph, leaving space for the remaining 2002 figures.                                                                        (3 marks)

b) Using the method of 2 quarterly centered moving,
i) determine the trend in the series and superimpose this on your graph in (a) above.                                                       (4 marks)

ii) determine the equation of the trend line above by considering only the first and last centered moving average value on your graph in (i) above.                                                                                                                                                                (3 marks)

c) Using an appropriate decomposition model to determine the seasonal variations in the data. Give reasons for your choice of model.                                                                                                                                                                                  (5 marks)

d) Use your analysis above to produce roughly forecasts of the mean number of absentees there will be in the remaining quarters of 2002. Comment on your forecast.                                                                                                                                   (5 marks)

a) Sketch Graph(s) to show the following critical points on a cost or revenue function:
i) Local Maximum Point                                                                    (1 mark)
ii) Absolute Maximum Point                                                             (1 mark)
iii) Local Minimum Point                                                                  (1 mark)
iv) Absolute Minimum Point                                                             (1 mark)
v) Point of inflexion                                                                           (2 marks)

b)

If the fixed market price of low grade steel is GH¢ 6.90 and the fixed market price of high grade steel is GH¢ 13.80.
Required:
i) Determine the number tons of low grade steel and high grade steel to be produced to maximize total revenue.            (10 marks)

ii) Determine the maximum total revenue.                                                                                                                         (4 marks)

Suppose that Mr. Kuu, a retired chartered accountant, is facing a decision about where to invest that small fortune that remains after he has deducted the anticipated expenses for the next year from the earnings from his consultancy job. An investment analyst has suggested to him two types of investment, and to help make the decision he obtained some rates of return from each type. He would like to know what he can expect by way of the return on his investment, as well as other types of information, such as whether the rates are spread out over a wide range (making the investment risky) or are grouped tightly together (indicating a relatively low risk). The returns for the two types of investments are listed here.

Required:
a) Draw histograms for each set of returns.                                                                                                                        (5 marks)

b) Compute the following measures of central tendency for the set of returns:
i) Mean                                                                                                                                                                                (3 marks)

ii) Median                                                                                                                                                                           (3 marks)

iii) Mode                                                                                                                                                                             (3 marks)

c) Compute the following measures of spread for the set of returns:
i) Standard deviation                                                                                                                                                            (3 marks)

ii) Coefficient of variation                                                                                                                                                   (2 marks)

d) Using (a), (b) and (c) above, which investment should Mr.Kuu choose and why?                                                         (1 mark)

Maame TorTor has just purchased a GH¢70,000.00 house and made a down Payment of GH¢15,000.00.
Required:
i) Determine how much money is needed to amortize (.i.e. pay monthly) the balance at 9% interest rate compounded annually for 25 years.                                                                                                                                                                         (5 marks)

ii) Determine the total interest for the 25 years.                                                                                                                  (2 marks)

iii) Determine after 5 years the equity she has in the house.                                                                                             (3 marks)

a) One of the most important application of annuities is the repayment of interest- bearing debts. These debts can be paid by making periodic deposits into a sinking fund which is used as a future date to pay the principal of the debt or by making periodic payments that cover the outstanding interest and the principle. This second method is called amortization.
(i) Explain the term annuities as used in the statement above.                                                                                            (2 marks)

(ii) What is a sinking fund?                                                                                                                                                 (2 marks)

(iii) When is a loan with a fixed rate of interest said to be amortized ?                                                                               (1 mark)

c) Maame TorTor borrows GH¢ 3000.00 and agrees to pay interest quarterly at an annual rate of 8%. At the same time, she set up a sinking fund in order to repay the loan at the end of 5 years. If sinking fund earns interest at the rate of 6% compounded semi-annually,
Required:
Determine the size of each semi-annual sinking fund deposit.                                                                                           (5 marks)

The Branch Manager of a building material production plant feels that the demand for Iron rods shipments may be related to the number of construction permits issued in the country during the previous quarter. The Manager has collected the data shown in the table below:

Required:
i) Use the normal equations of the least square regression method to derive a regression forecasting equation for the data.  (9 marks)

ii) Interpret your regression coefficient in (i) above.                                                                                                           (1 marks)

iii) Using the regression line in (a) above, determine a point estimate for Iron Rods when the number of construction permits is 30.                                                                                                                                                                                        (2 marks)

iv) Is your estimate in (iii) above reliable? Give reason(s) for your answer.                                                                      (2 marks)

v) Calculate the coefficient of determination and interpret it.                                                                                           (6 marks)

JinJin Company Limited makes two types of leather belts Type Superior and Type Standard. Type Superior is a highly quality and Type Standard is of lower quality. The respective profits are GHp 40 and GHp 30 per belt. The production of each of Type Superior requires twice as much time as a belt of Type Standard, and if all belts were of Type Standard, the company could make 1000 belts per day. The supply of leather is sufficient for only 800 belts per day (both Type Superior and Type Standard combined). Belt Type Superior requires a fancy buckle and only 400 of these are available per day. There are only 700 buckles a day available for belt Type Standard. If the aim is to determine how many units of the two types of belts the company should manufacture in order to have the maximum overall profit:

Required:
a) Formulate this problem as a Linear Programming Model.

b) Set up the initial Simplex Tableau.                                                                                                                                 (4 marks)

c) Solve your Tableau in (b) above.                                                                                                                                    (8 marks)

d) Interpret your final Simplex Tableau.                                                                                                                            (4 marks)

a) Distinguish between the following terms as used in probability:
i) Independents Events and Dependent Events.                                                                                                                   (2 marks)

ii) Mutually exclusive Events and Exhaustive Events.                                                                                                        (2 marks)

iii) Marginal Probability and Joint Probability.                                                                                                                   (2 marks)

b) Mr Agbagba, an ICAG qualified member and his wife an ICAEW qualified member attended an interview for two vacancies for the post of College Finance Officer at a Private University. The probability of the interview panel selecting the man is 1/7 and that of the wife is 1/5.
Required:
Assuming the event selecting a man and selecting a woman are independent, determine the probability that;
i) both of them will be selected,

ii) only one of them will be selected,

iii) none of them will be selected.                                                                                                                                       (3 marks)

c) If selected by the panel the probability that an ICAG qualified member will remain with the Private University is 0.6, and the probability that a Chartered Accountant earns more than GH¢5,000.00 per month in the university is 0.5. If the probability that Mr Agbagba will remain with the university or he will earn more than GH¢5,000.00 per month is 0.7;
Required:
Calculate the probability that he will earn more than GH¢5,000.00 per month given that he is a Chartered Accountant who will stay with the university.                                                                                                                                                       (5 marks)

A loan of GH¢3,000 at an effective annual interest rate of i = 2% is amortized by means of 12 annual payments, beginning a year after the loan is taken.
Hint: The schedule should have the following columns: Payment, Interest Due, Principal Repaid and Outstanding Balance.
Required:
Construct an amortization schedule.