An advertising agency wishes to reach two types of audiences: Customers with annual income greater than GH¢ 15,000 (target audience A) and customers with annual income less than GH¢15,000 ( target audience B). The total advertising budget is GH¢ 200,000. One programme on TV advertising costs GH¢50,000; one programme on radio advertising costs GH¢20,000. For contract reasons, at least three programmes ought to be on TV, and the number of radio programmes must be limited to five. Surveys indicate that a single TV programme reaches 450,000 customers in target audience A and 50,000 in target audience B. One radio programme reaches 20,000 in target audience A and 80,000 in target audience B.
Required:
i) Formulate the linear programming problem.                                                                                                                  (4 marks)

ii) Construct the initial simplest tableau.                                                                                                                            (4 marks)

iii) Perform the first iteration.                                                                                                                                             (4 marks)

iv) Determine the media mix to maximize the total reach.                                                                                                 (4 marks)

v) Determine the shadow prices of the binding constraint.                                                                                                 (4 marks)

The Asogli Company Ltd has been offered the following alternative terms for a one year loan to be repayable plus the interest in full at the end of the year:
i) 2.5% per month compounded monthly
ii) 10% per six months compounded six-monthly.
Required:
Calculate, for each alternative the annual percentage rate of interest. Recommend one of the alternatives and explain why.  (10 marks)

a) Accra Junction Mall sells apples either for GH¢10 per kg or in bulk GH¢180 per 20 kg. What is the percentage saving per kg from buying in bulk?                                                                                                                                                           (2 marks)

b) Solve the following expression;                                                                                                                                      (3 marks)

i)

ii)

c) A compound house at Ashaiman has a simple meter. There are 5 units’ chamber and hall within the compound. The total electricity bill submitted by ECG for the month of September 2017 was GH¢2,700. The outstanding bill on the month of August 2017 was GH¢1,000.
Required:
Calculate the bill for each tenant for the month of September 2017 if the tenants had agreed to share the bill in the ratio 2:3:4:5:6.                                                                                                                                                                              (5 marks)

The following data gives how much 10 students of ICAG spend on TroTro to the Institute and food weekly .

Required:
a) Using a graph paper, construct a scatter diagram of the data.                                                                                         (4 marks)

b) Determine, the correlation coeficient.                                                                                                                             (4 marks)

c) Calculate, the coefficient of determination of the data and interpret its value.                                                               (4 marks)

d) Determine the regression line of y on x , and interpret the coefficient.                                                                          (8 marks)

a) Consider people’s preferences in terms of chocolate and their eye colour, presented as probability tree diagram below:

If 30% of people have brown eyes, 40% have green eyes and the remaining people have blue eyes, and it is found that 70% prefer milk chocolate , 10% prefer white chocolate and the remaining prefer plain chocolate, using the tree diagram above.

Required:
Calculate the probability that a person:
i) P ( Prefer plain Chocolate and has Brown Eyes)                                                                                               (1.5 marks)

ii) P ( Prefer milk Chocolate and has Brown Eyes)                                                                                               (1.5 marks)

iii) P ( Prefer white Chocolate and has Brown Eyes)                                                                                             (1.5 marks)

iv) P ( Prefer plain Chocolate and has Green Eyes)                                                                                               (1.5 marks)

v) P ( Prefer milk Chocolate and has Green Eyes)                                                                                                 (1.5 marks)

vi) P ( Prefer white Chocolate and has Green Eyes)                                                                                               (1.5 marks)

vii) P ( Prefer plain Chocolate and has Blue Eyes)                                                                                                 (1.5 marks)

viii) P ( Prefer milk Chocolate and has Blue Eyes)                                                                                                (1.5 marks)

ix) P ( Prefer white Chocolate and has Blue Eyes)                                                                                                 (1.5 marks)

b) If three fair coins are tossed,
Required:
Determine, the probabilities of
i) getting two heads and a tail                                                                                                                                  (3.5 marks)

ii) getting three tails                                                                                                                                                 (3 marks)

The mileages recorded for a sample of company vehicles during a given week gave the following data:

Required:
a) Draw the frequency table of this data given a class size of 5.                                                                                         (6 marks)

b) Determine mean, median and mode for the data and comment on the distribution of data.                                           (6 marks)

c) Compute the quartile deviation.                                                                                                                                      (4 marks)

d) Determine the standard deviation for the data.                                                                                                               (4 marks)

a) A particular linear programming problem is formulated as follows:
Minimize z = 2500x + 3500y
Subject to constraint:

Required:
i) Draw these constraints on the same graph paper.                                                                                                           (6 marks)

ii) Determine the optimum solution.                                                                                                                                  (6 marks)

b) Managers within a subsidiary company in a conglomerate want to know how to maximize the profit from two types of products X and Y. Each product X requires one hour of labour and six litres of molding material, whereas each product Y requires two hours of labour and five litres of molding material. The total labour hours available for each week is 40 and the total amount of molding material each week is 150. The profit contribution from product X is GH¢20 and from product Y is GH¢ 30.
Required:
Formulate, the linear programming model for the problem.                                                                                              (8 marks)

a) The AXM manufacturing company has determined that the cost function for producing a particular type of pavement block is given by:

where x is measured in number of units and C(x) in GH¢.

Required:
i) Calculate the derivative of C(x) with respect to x .                                                                                                          (5 marks)

ii) Determine how quickly the cost is changing at x =1000.                                                                                               (4 marks)

b) At the Zee manufacturing company, the marginal cost for producing x gears, measured in hundreds is

MC =10+0.1x .
If the fixed cost (the cost of producing zero items) is GH¢3000.
Required:
Determine the cost for manufacturing 5000 gears.                                                                                                            (11 marks)

Required:
Determine the most preferred business opportunity if:

[ NB: You are required to discount these future sums by using the interest rate of 8%. ]

i) GH¢7000.00 is paid in 4 years’ time.                                                                                                                             (7 marks)

ii) GH¢8000.00 is paid in 6 years’ time.                                                                                                                             (7 marks)

Calculate the accumulated amount if GH¢2500.00 were invested at 18% compound interest for a period of six years.        (6 marks)