Accra brewery Ltd is planning a marketing campaign for its new product targeted at the Youth, the Middle Aged and the Aged of a small town. The Population of the town is 3000 which is equally divided between the youth and middle aged and the aged. The cost per minute advertisement on radio and TV is GHC 1000 and GHC 1300 respectively. In general, a minute of radio advertisement can reach 4%. 3.2% and 4% of the youth, middle aged and the aged population respectively, whiles a minute advertisement on TV can reach 1.5%. 1.6% and 3% of the youth, middle aged and the aged respectively. Accra Brewery will want to reach at least 10% of the youth population, at least 32% and at most 40% of the middle-aged population, and at least 60% of the aged population. a) Formulate a linear program to determine the optimum mix of the radio and TV adverts that should be done to achieve the company objective while minimizing the cost involved. b) Solve the LP problem in (a) above using graphical approach to determine the optimal number of minutes of advertisement on both radio and TV.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Accra brewery Ltd is planning a marketing campaign for its new product targeted at the Youth, the Middle Aged and the Aged of a small town. The Population of the town is 3000 which is equally divided between the youth and middle aged and the aged. The cost per minute advertisement on radio and TV is GHC 1000 and GHC 1300 respectively. In general, a minute of radio advertisement can reach 4%. 3.2% and 4% of the youth, middle aged and the aged population respectively, whiles a minute advertisement on TV can reach 1.5%. 1.6% and 3% of the youth, middle aged and the aged respectively. Accra Brewery will want to reach at least 10% of the youth population, at least 32% and at most 40% of the middle-aged population, and at least 60% of the aged population.
a) Formulate a linear program to determine the optimum mix of the radio and TV adverts that should be done to achieve the company objective while minimizing the cost involved.
b) Solve the LP problem in (a) above using graphical approach to determine the optimal number of minutes of advertisement on both radio and TV.
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