# SOLVED:Linear programming model

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## Description

(a) Define the decision variables and write the linear programming model for the problem in the space provided below
product 1= x1 product 2= x2
Assembly Line 1: 10*x1+14*x2<=100
Assembly Line 2: 7*x1+3*x2<=42
Maximise: 6*x1+4*x2
(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?

(a) Define the decision variables and write the linear programming model for the problem in the space provided below
Chairs =x1 Tables=x2
Hours of Labour 8*x1+10*x2<=80
Wood Available 2*x1+6*x2<=36
Number of chair x<=6
Profit 400*x1+100*x2
(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
(c’)  Write all the vertices of the feasible region and identify the optimal vertex
What is the optimal objective function value?

(a) Define the decision variables and write the linear programming model for the problem in the space provided below
Ingredient 1 x1
Ingredient 2 x2
3×1+x2>=6 x1>=0
x1+x2>=4 x2>=0
2×1+6×2>=12
minimum cost 80×1+50×2
(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?

 (a) Define the decision variables and write the linear programming model for the problem in the space provided below Coats=X1 Slacks=X2 Clothier 3*X1+5*X2<=150 Labour Hours 10*X1+4*X2<=200 maximise Profit 50*X1+40*X2 (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?