**1.Text**

The company produces and sells iron bars in several widths. Customers can order bars of 20 cm (type A), 10 cm (type B) or 5 cm (type C) long. The customers’ orders are in Table 1. The standard width of manufactured bars is 50 cm, and the smaller lengths are cut from the standard bars. There are several cutting plans for getting the smaller lengths - Table 2. The goal of the company is to satisfy all demands for small bars using minimal number or the source material i.e. 50 cm long bars.

**2. Tables
and pictures**

Length | Bars ordered |

A-20 cm | 350 |

B-10 cm | 180 |

C-5 cm | 220 |

**Table 1: Orders for cut bars**

C | B | B | C | B | C |

C | C | C | |||

A | B | A | C | B | C |

C | C | ||||

B | B | B | C | ||

C | |||||

A | A | A | A | B | C |

C | |||||

B | C | ||||

C | |||||

Plan No.1 | Plan No.2 | Plan No.3 | Plan No.4 | Plan No.5 | Plan No.6 |

**Picture 1:Cutting plans**

There are 6 bars of the source material cut according different plans. The manufacturer designs these plans. Naturally there are not all possible plans but only some promising ones ( with no or minimal scrap, containing all demanded shorter lengths). Not all of these plans will be probably used in optimal solution.

From the picture can be understand that for example
using plan No.1 we get 2 pieces of A and 2 pieces of C –all plans see Table
2.

Plan 1 | Plan 2 | Plan 3 | Plan 4 | Plan 5 | Plan 6 | |

Pieces of A | 2 | 1 | 2 | 1 | 0 | 0 |

Pieces of B | 0 | 3 | 1 | 1 | 5 | 0 |

Pieces of C | 2 | 0 | 0 | 4 | 0 | 10 |

**Table 2: Cutting plans**