1. Find the optimal solution of the following linear programming problem using the Corner Points method.

Min 2x + 2y

Subject to

x + y > 5

x + 2y < 8

x, y > 0

2. Find the optimal solution of the following linear programming problem using the Iso-Profit (objective function) Line method.

Min 4x + 5y

Subject to

2x + y > 20

x + 3y < 30

x, y > 0

3. Solve the following linear programming problem.

Min 40x + 25y

Subject to

2x + 3y > 45

x + y < 10

x, y > 0

4. Solve the following linear programming problem.

Max 7x + 6y

Subject to

2x + y > 16

x > 4

y > 5

x, y > 0

5. A cereal company makes a cereal from two ingredients: wheat and oats. Each ingredient provides two essential nutrients: vitamin A and vitamin B. The company wants to know how many ounces of wheat and oats to include in each box of cereal so that the minimum requirements of 45 milligrams of vitamin A and 25 milligrams of vitamin B are satisfied. An ounce of wheat provides 12 milligrams of vitamin A and 6 milligrams of vitamin B. An ounce of oats provides 8 milligrams of vitamin A and 7 milligram of vitamin B. An ounce of wheat costs $0.05 and an ounce of oats costs $0.08. The company wants to minimize the total cost of production.

Formulate the above situation as a linear programming problem. Do NOT solve after formulating.

Note: Some of the questions above require drawing graphs. Here is a list of options for you to include a graph in your answer.

Draw the graph using MS Paint or CorelDraw or some other software. Copy the graph in a MS Word file and post the file on the course website in appropriate category.

OR

Draw the graph by hand on a paper, scan it or take a photo and post it with your answer.

OR

Draw the graph by hand on a paper and describe the graph in words in your answer.

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Take notes on the reading that are organized in a visually memorable way. Your notes must define key concepts and capture key points from the reading.

Just need to take note of pages 154 – 158

You can just note the main point of those pages and a very short summary with bullet point.

No need to cite any main point

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