# (b) Sketch the feasible region. Give your answer in the worksheet named P1-Graph

## P1

 (a) Define the decision variables and write the linear programming model for the problem in the space provided below (b) Sketch the feasible region. Give your answer in the worksheet named P1-Graph (i) You can use QM for Windows to get the graph, copy and paste it onto the worksheet named P1-Graph OR (ii) You can sketch the feasible region on paper, scan and save it in your computer. Copy the image (i.e. graph) and paste it onto the worksheet named P1-Graph (c’) Write all the vertices of the feasible region and identify the optimal vertex What is the optimal objective function value? Vertex x1 x2 x1 x2 1 optimal vertex 2 3 optimal objective fuction value

## P2

 (a) Define the decision variables and write the linear programming model for the problem in the space provided below (b) Sketch the feasible region. Give your answer in the worksheet named P2-Graph (i) You can use QM for Windows to get the graph, copy and paste it onto the worksheet named P2-Graph OR (ii) You can sketch the feasible region on paper, scan and save it in your computer. Copy the image (Graph) and paste it onto the worksheet named P2-Graph Write all the vertices of the feasible region and identify the optimal vertex What is the optimal objective function value? Vertex x1 x2 x1 x2 1 optimal vertex 2 3 optimal objective fuction value 4 5 (c’) How much labor and wood will be unused if the optimal number of chairs and tables are used? Provide your answer in the space below

## P3

 (a) Define the decision variables and write the linear programming model for the problem in the space provided below (b) Sketch the feasible region. Give your answer in the worksheet named P4-Graph (i) You can use QM for Windows to get the graph, copy and paste it onto the worksheet named P4-Graph OR (ii) You can sketch the feasible region on paper, scan and save it in your computer. Copy the image (Graph) and paste it onto the worksheet named P4-Graph (c’) Write all the vertices of the feasible region and identify the optimal vertex What is the optimal objective function value? Vertex x1 x2 x1 x2 1 optimal vertex 2 3 optimal objective fuction value

## P4

 (a) Sketch the feasible region. Give your answer in the worksheet named P5-Graph (i) You can use QM for Windows to get the graph, copy and paste it onto the worksheet named P5-Graph OR (ii) You can sketch the feasible region on paper, scan and save it in your computer. Copy the image (Graph) and paste it onto the worksheet named P5-Graph (b) Write all the vertices of the feasible region and identify the optimal vertex What is the optimal objective function value? Vertex x1 x2 x1 x2 1 optimal vertex 2 3 optimal objective fuction value