# Lp Graphical Methods For Minimization Problems And Special Situations

### Question Description

For this discussion topic each student is required to have at least 2 postings: One answering at least one of the questions and a second responding to another student’s posting. Please select a question that has not been answered by the time you post your response. You can select any question to answer once all questions are answered. Please do not copy another student’s posting.

This discussion will close at midnight Sunday, September 23rd.

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 50 milligrams of vitamin A and 15 milligrams of vitamin B are satisfied. An ounce of wheat provides 10 milligrams of vitamin A and 2 milligrams of vitamin B. An ounce of oats provides 5 milligrams of vitamin A and 1 milligram of vitamin B. An ounce of wheat costs \$0.03 and an ounce of oats costs \$0.06. 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 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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