LINEAR PROGRAMMING IN GAME THEORY ASSIGNMENT

a. MR UBONG'S DIET

Mr Ubong eats a mix of Cereal A and Cereal B for breakfast.

The amount of calories, sodium and protein per ounce for each

Cereal is shown in the table below. Mr Ubong's breakfast

should provide at least 480 calories but less than or equal to

700 milligrams of sodium. Mr Ubong would like to maximise

the amount of protein in his breakfast mix.

Using graphical linear programming method, determine the

ideal mix for Mr Ubong

CEREAL A CEREAL B

Calories (per ounce) 100 140

Sodium (mg per ounce) 150 190

Protein (g per ounce) 9 10

b. STEVE AND THE FIREFIGHTER EXAM

Steve is taking an exam to become a volunteer firefighter. The

exam has 10 essay questions and 50 short questions. He has

90 minutes to take the exam. The essay questions are worth

20 marks each and the short questions are worth 5 marks

each. An essay question takes 10 minutes to answer and a

short question takes 2 minutes.

Steve must do at least 3 essay questions and at least 10 short

questions. He knows the material well enough to get full

marks on all the questions he attempts, and naturally wants to

maximise his score.

Frame this as a linear programming problem and solve

graphically

c. MADAM AISHA'S CAMPAIGN BUDGET

Madam Aisha is budgeting for her media campaign in an upcoming

election. She will distribute her funds between TV ads and radio

ads. She has been given the following advice by her campaign

manager:

She should run at least 120 TV ads and at least 30 radio ads

The number of TV ads she runs should be at least twice the

number of radio ads she runs, but not more than three times the

number of radio ads she runs

The cost of a TV ad is $8000 and the cost of a radio ad is $2000.

What combination of TV and radio ads should she choose to

minimise the cost of her media campaign?

Frame this as a linear programming problem and solve graphically