Two Phase method
Enviado por Jam Abdón Abad Martínez Chavero • 22 de Agosto de 2018 • Documentos de Investigación • 291 Palabras (2 Páginas) • 139 Visitas
Names: 1) ___________________________________________
2) ___________________________________________
Problem 1
A manufacturing firm produces two products using labour and material. The company has a contract to produce 5 units of product 1 and 12 of product 2. The company has developed the following linear programming model to determine the number of units of product 1 () and product 2 () to produce to maximize profit.[pic 1][pic 2]
Maximize Z = 40x1+60x2 | |
Subject to 1x1 + 2x2 ≤ 30 | kg (Material) |
4x1 + 4x2 ≤ 72 | hr (Labour) |
x1 ≥ 5 | units (contracted demand) |
x2 ≥ 12 | units (contracted demand) |
x1, x2 ≥ 0 |
Solve the problem using the two phase method. Please, observe that this is a maximization problem; that means that in phase 2 of the method you need to apply the appropriate optimality criterion (30 points). You can use Excel and then copy the results to the tables below.
Variables | Z | x1 | x2 | s1 | s2 | e3 | e4 | a3 | a4 | RHS | BV |
Obj. Function | 1 | 0 | 0 | 30 | 0 | -10 | 0 | 10 | 0 | 950 | Z |
Constraints | 0 | 0 | 0.5 | 0 | 0.5 | 1 | -0.5 | -1 | 0.5 | e4 | |
0 | 0 | -2 | 1 | 2 | 0 | -2 | 0 | 2 | s2 | ||
1 | 0 | 0 | 0 | -1 | 0 | 1 | 0 | 5 | x1 | ||
0 | 1 | 0.5 | 0 | 0.5 | 0 | -0.5 | 0 | 12.5 | x2 | ||
Problem 2
Solve the following problem using the two phase method (25 points). You can use Excel and then copy the results to the tables below.
Min Z = 0.05x1+0.10x2 |
Subject to 6x1+2x2 ≥ 36 |
5x1+5x2 = 50 |
Variables | Z | x1 | x2 | e1 | a1 | a2 | RHS | BV |
Obj. Function | 1 | 0 | -0.05 | 0 | 0 | 0.01 | 0.5 | Z |
Constraints | 1 | 1 | 0 | 0 | 0.2 | 10 | x1 | |
0 | 4 | 1 | -1 | 1.2 | 24 | e1 | ||
Problem 3
Solve the following problem using the two phase method (25 points). You can use Excel and then copy the results to the tables below.
Minimize Z= 120x1+40x2+240x3 | |
Subject to 4x1 + 1x2 + 3x3 ≥ | 27 |
2x1 + 6x2 + 3x3 ≥ | 30 |
x1, x2, x3 ≥ | 0 |
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