Accra Brewery Ltd is planning a one week advertising 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, the Middle-Aged, and the Aged. Two television stations (TV3 and GTV), and one radio station (Adom Radio) are under consideration. The cost per minute advertisement on TV3, GTV, and Adom Radio is GH¢1600, GH¢1400, and GH¢1000 respectively. Information available indicates that, a minute of advertisement on TV3 can reach 4%, 3.2%, and 4% of the Youth, Middle-Aged, and the Aged population respectively, whiles a minute advertisement on GTV can reach 1.5%, 1.6%, and 3% of the Youth, Middle-Aged, and the Aged respectively. On the other hand, a minute advertisement on Adom Radio can reach 1%, 2%, and 4% 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% of the Middle-Aged population, and at least 60% of the Aged population. Also, there must be no more than 9 minutes of advertisement within the week on Adom Radio.

Formulate a linear program that can be used to determine the number of minutes of advertisement to be placed on TV3, GTV, and Adom Radio, and use it to answer the following questions.

The following table gives a portion of the sensitivity report of the problem above when solved using Excel solver add-in. Answer the following questions:

Variable
Name	Final Value	Reduced Cost	Objective Coefficient	Allowable Increase	Allowable Decrease
TV3	6	0	1600	266.66	600
GTV	0	200	1400	1.00E+30	200
Adom Radio	9	0	1000	600	1.00E+30

Constraints
Name	Final Value	Shadow Price	Constraint R.H. Side	Allowable Increase	Allowable Decrease
Aged	600	40	600	1.00E+30	65
Limit on Radio	9	-400	9	4.33	9

1. The number of minutes of advertisement to be placed on TV3 is Blank 1. Fill in the blank, read surrounding text. minutes.

2. The number of minutes of advertisement to be placed on GTV is Blank 2. Fill in the blank, read surrounding text. minutes.

3. The number of minutes of advertisement to be placed on Adom Radio is Blank 3. Fill in the blank, read surrounding text. minutes.  

4. The total cost of the advertising campaign if the optimal plan obtained is followed is GHS Blank 4. Fill in the blank, read surrounding text. .  

5. Let TV3, GTV, and Adom Radio be represented by the numerical values 1, 2, and 3 respectively. The medium of advertisement (using the numerical values) not recommended is Blank 5. Fill in the blank, read surrounding text. .

6. If Accra Brewery Ltd does not follow the optimal allocation advise given by the linear program, and instead goes ahead to allocate 5 minutes of advertisement on the medium of advertisement not suggested by the LP (i.e. where allocation is 0 minutes), the total advertisement cost will increase by GHS Blank 6. Fill in the blank, read surrounding text. .

7. Let the words ‘Yes’ and ‘No’ be represented by the numerical values 1 and 2 respectively. Will the optimal plan suggested change if GTV reduces it per unit charge by GH¢220? Blank 7. Fill in the blank, read surrounding text. .

8. The shadow price of the limit of minutes of radio advertisement can be interpreted as (fill in the numerical answers):

For every minute of radio advertisement above 9 minutes, the advertising cost (in relation to the number of people to be reached) will reduce by GHS Blank 8. Fill in the blank, read surrounding text. . This is true for an increase not more than Blank 9. Fill in the blank, read surrounding text. minutes.

On the other hand, whenever the limit on the number of minutes of advertisement on radio is tightened by a minute, the advertising cost (in relation to the number of people to be reached) will increase by GHS Blank 10. Fill in the blank, read surrounding text. . This is true for a decrease of not more than Blank 11. Fill in the blank, read surrounding text. minutes.

9. If the minutes of advertisement on radio were to be increased by 5 minutes, the total advertisement cost will reduce by GHS Blank 12. Fill in the blank, read surrounding text.

10. The shadow price of the constraint on the Aged population to be reached can be interpreted as (fill in the numerical answers):

Each unit increase in the number of Aged population to be reached will lead to an increase of GHS Blank 13. Fill in the blank, read surrounding text. in advertising cost. This is true for any increase.

Likewise, each unit decrease in the number of Aged population will lead to reduction of GHS Blank 14. Fill in the blank, read surrounding text. in advertising cost. This is true for a decrease not more than Blank 15. Fill in the blank, read surrounding text. people.

11. The number of youth reached by either TV or radio is Blank 16. Fill in the blank, read surrounding text.

12. The number of the middle-aged reached by either TV or radio is Blank 17. Fill in the blank, read surrounding text.

13. The number of the Aged reached by either TV or radio is Blank 18. Fill in the blank, read surrounding text.

Answer rating: 100% (QA)

Let 29 denote the number of minutes of advertisements to be placed on TV3 GTV and Adom ... View the full answer