# LP: Introduction and Graphical Methods for Maximization Problems

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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 16^{th}.

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

Max 3x + 5y

Subject to

4x + y __>__ 4

3x + 2y __<__ 12

x, y __>__ 0

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

Max 3x + 5y

Subject to

4x + y __>__ 4

3x + 2y __<__ 12

x, y __>__ 0

3. Write the following linear programming problem in standard form.

Max 2x + y

Subject to

x + y __>__ 2

3x + 4y __<__ 12

x, y __>__ 0

4. For the linear programming problem given in Question 3, the optimal solution is given by x=4 and y=0. Do a constraint analysis (that is, find the values of slack and surplus variables) for the optimal solution.

5. The Pinewood Furniture Company produces chairs and tables from two resources – labor and wood. The company has 80 hours of labor and 36 board-ft. of wood available each day. Demand for chairs is limited to 6 per day. Each chair requires 8 hours of labor and 2 board-ft. of wood, whereas a table requires 10 hours of labor and 6 board-ft. of wood. The profit derived from each chair is $400 and from each table, $100. The company wants to determine the number of chairs and tables to produce each day in order to maximize profit.

Formulate a linear programming model for the above situation by determining

(a) The decision variables.

(b) The objective function.

(c) All the constraints.

**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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