# (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 |

## P1-Graph

## 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 |

## P2-Graph

## 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 |

## P3-Graph

## 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 |