The marginal revenue function of a manufacturing company is given by: The marginal cost function is given by:  Let x be the number of items either produced or sold.
Required:
i) Calculate the revenue generated when 50 items are sold.                                                                                              (2 marks)

ii) Calculate the number of items that will yield maximum revenue.                                                                                (4 marks)

iii) Calculate the total revenue if 100 items are produced.                                                                                                (4 marks)

iv) Calculate the total profit for the 100 items.                                                                                                                  (4 marks)

v) If the tax of 20% is imposed on each item produced, find the cost of 100 items.                                                         (6 marks)

A Ghanaian student studying abroad wants to develop an empirical model for energy consumption (in kilowatts per day) as a function of the daily high temperature (in degrees Celsius) in winter. For nine days the following information was obtained:

Required:
a) Identify the response and predictor variables, based on the purpose for developing the regression model.                  (2 marks)

b) Determine the coefficient of regression and the regression constant. Give your values to 2 decimal places.                (5 marks)

c) Interpret your results in b) above.                                                                                                                                   (3 marks)

d) Write the equation of the regression line of energy use on temperature in the form y=a+bx.                                       (2 marks)

e) Estimate the student’s daily energy consumption when the daily high temperature is 2 degrees Celsius.                     (2 marks)

f) Determine the standard error of estimate.                                                                                                                        (6 marks)

The Managing Director of a small manufacturing company is considering buying a piece of machinery which costs GH¢15,000.
Required:
If the machine is to be purchased by taking a five year loan at 9% per annum which will be paid off in five equal annual instalments (starting a year after the loan is taken out), calculate the size of each instalment to the nearest whole number.    (6 marks)

You have received a prize amount of GH¢5,000 and you wish to invest it for five years. The two alternatives are to use a bank account where the 14% per annum gross rate is compounded monthly or a savings fund where the 14.5% per annum gross rate is compounded annually.
Required:
i) Calculate the size of each fund at the end of the five years. (Ignore tax considerations).                                               (8 marks)

ii) Calculate the effective annual interest rate of the bank account investment.                                                                 (4 marks)

iii) Advise your client on the basis of your calculations.                                                                                                    (2 marks)

Alpha Transport Company buys a vehicle for GH¢265,000. The value of the vehicle depreciates on a reducing balance basis at 17% per annum. The company plans to replace this vehicle in 5 years’ time and they expect the price of a new vehicle to increase annually by 12%.
Required:
i) Calculate the book value of the vehicle in five years’ time.                                                                                             (3 marks)

ii) Determine the amount of money needed in the sinking fund for the company to be able to afford a new vehicle in five years’ time.                                                                                                                                                                                    (3 marks)

iii) Calculate the required monthly deposits if the sinking fund earns an interest rate of 11% per annum compounded monthly. (3 marks)

Every Monday, Kwei puts GH¢30 into a savings account at the Ring Bank, which accrues interest of 6.92% per annum compounded weekly.
Required:
i) Draw a cash flow timeline showing the payments, the interest rate and the present values for the first 4 payments.    (3 marks)

ii) Determine how long it will take Kwei’s account to reach a balance of GH¢4,397.53. Convert your answer into number of years and days to the nearest integer.                                                                                                                                  (6 marks)

iii) Determine how much interest Kwei will receive from the bank during the period of his investment.                         (2 marks)

a) Distinguish between marginal cost and average cost in production.                                                                               (2 marks)

The company has set production limit to 10,000 Cans and it sells all the Cans that are produced.
Required:
i) Derive an expression for marginal cost, marginal revenue and marginal profit.                                                             (4 marks)

ii) Determine the cost, revenue and profit when the 2501st Can is produced and sold.                                                     (3 marks)

iii) Determine the cost, revenue and profit when the 7501st Can is produced and sold.                                                    (3 marks)

iv) Advise the company whether to produce the 2501st Can or the 7501st Can.                                                                (2 marks)

c) If, after expanding its facilities, the company is capable of producing 60,000 Cans in a day and the total daily cost is given by

Required:
How many Cans per day should they produce in order to minimize production costs?                                                     (6 marks)

The distribution of the total loan amounts defaulted by customers of a bank annually is approximated by a normal distribution. An average default amount is GH¢1.50 million and the standard deviation is GH¢0.50 million.
Required:
a) Determine the probability that the total loan amount defaulted exceeds GH¢1.50 million.                                           (3 marks)

b) Determine the probability that the total loan amount defaulted is between GH¢0.86 million and GH¢0.90 million.   (4 marks)

c) Determine the probability that the total amount defaulted is at most GH¢2million.                                                      (4 marks)

d) Determine the amount to be allowed per annum for loan defaults if 1% of actual defaults exceed this amount.          (3 marks)

e) Determine the lower quartile of the distribution of total loan amounts defaulted.                                                          (3 marks)

f) Determine the upper quartile of the distribution of total loan amounts defaulted.                                                          (3 marks)

Data on access time, in minutes, to a medical consultant who charges by the hour was recorded by his accountant’s assistant over a period of one week. Using a class width of 4 minutes, the following frequency distribution table was obtained:

Required:
a) Using a graph sheet draw a less than or a greater than (more than) cumulative frequency curve (ogive) of the data.   (6 marks)

b) From the ogive in (a) above estimate the median access time.                                                                                       (2 marks)

c) Calculate the mean and the mode of the access times.                                                                                                    (6 marks)

d) Calculate the standard deviation of the distribution.                                                                                                       (4 marks)

e) Using, the values in (b) and (c) above, comment on the skewness of the distribution.                                                  (2 marks)

A small business is interested in the relationship between the number of hits on its web site ( measured by number of visitors that have used the main menu) and the level of web site promotion (in GH¢ 00s). The table below gives the figures for the last six months;

Required:
a) Graph the number of web site hits against web site promotion.                                                                                     (2 marks)

b) Comment on any possible relationship in (a) above.                                                                                                      (2 marks)

c) Calculate the correlation coefficient and give an interpretation to its value.                                                                  (5 marks)

d) Determine the regression line.                                                                                                                                         (5 marks)

e) Using the regression line found in part (d) above, predict the number of web site hit if the level of monthly promotion were increased to GH¢200.                                                                                                                                                          (2 marks)

f) Comment on the reliability of your prediction in (e) above.                                                                                             (1 mark)

g) Comment on the simple forecasting model you have developed above.                                                                        (3 marks)