I. 159. A lumber yard sells wooden boards of fixed length, but their cross-section can be freely determined by the customers. The yard cuts the appropriate boards out of trunks of different diameter. Due to the manufacturing technology they cut only right prism shaped, parallel boards of the same size out of a given trunk. The figure shows a possible arrangement.
You should prepare an Excel sheet that chooses between three cutting sizes so that the waste of wood is minimal when the boards are manufactured. Your file should contain two sheets, the first specifying the three possible cutting sizes, e.g. 10 cm×20 cm, 15 cm×15 cm and 12 cm×17 cm, further, the diameter of the trunk, e.g. 87 cm. Your answer should also appear here, giving which cutting size is optimal to that diameter. Auxiliary computations should be performed on the second sheet.
We will take into account the user-friendliness of your sheets (e.g. cell protection) too. (If cell protection is applied, there is no need to specify a password.)
The worksheet with your solution (i159.xls, ) should be submitted.
Deadline expired on 15 May 2007.
Google Translation (Sorry, the solution is published in Hungarian only.)
Kovács Péter (Szolnok, Verseghy Ferenc Gimnázium) megoldása. Köztünk szólva, a felületet még lehetett volna csicsázni kicsit, de a táblázatos elrendezés, és a megfelelő cellák védelme a fontos.