Linear Programming

LP: THE GRAPHICAL METHOD

Today’s Topic:

1. A Simple LP Example

2. Graphical solution of LP

3. Special Cases

4. Graphical Sensitivity Analysis

1. Change of an objective function coefficient

Change of a right-hand-side

Simultaneous changes of several coefficients

1. A Simple LP Example

RMC, Inc. is a firm that produces chemical-based products. Three raw materials are used to produce two products. The material requirements per ton are shown below.

|Product |Material 1 |Material 2 |Material 3 |

|Fuel additive |2/5 |0 |3/5 |

|Solvent base |1/2 |1/5 |3/10 |

For the current production period, RMC has available the following quantities of each raw material. Because of spoilage, any materials not used for current production must be discarded.

|Material |Material 1 |Material 2 |Material 3 |

|Available |20 |5 |21 |

If the contribution to profit is $40 for each ton of fuel additive and $30 for each ton of solvent base, how many tons of each product should be produced in order to maximize the total contribution to profit?

-- LP formulation

Decision variables:

2. Objective function:

3. Constraints:

-- Interpretation

feasible vs. infeasible

feasible solution vs. optimal solution

slack vs. surplus

| |slack = rhs - lhs |surplus = lhs - rhs |

| |≤ constraints |≥ constraints |

|0 |all resources used...