MathCAD




Example 8. As the author sold the programs - 2


the supply department MPEI cost 14 600 roubles for litre and was bottled to the tares (to the drums it is the gists slang which I have picked up in Kotovsk). The drums volume was 15 and 55 litres. Empty drums cost. 24 and 30 thousand roubles correspondingly. The sales departments worker of PVP (her name was Olga) making out the waybill on the computer asked what capacities (pardon drums) I would take paint. The flair of old collector of the computer etudes suggested to me that there is typical and main thing real problem of linear programming where we have to maximize the criterion function. This function is the summary volume of paint, the variables are the quantity of full drums of 15 and 55 litres that we had to take and three limitations (1) paints price can not exceed stipulated with Tambour-power 14 million roubles, (2) it is not allowed to take not full jar (it is the limitation to integer numbers) and (3) quantity of the jars different capacity is not allowed to be negative numbers[5]. Olga offered to help me with solving this optimization problem. With help of calculator[6]

she tossed in that I had to take 16 big and 2 small drums containing 910 litres of paint the sum of 13 million 814 thousand roubles. Remembered how I awfully argued in Tambov-power and nevertheless increased the programs price from 12 to 14 million roubles I asked Olga if I could not lose 186 thousand i.e. not leave them Tambov-power. She answered negatively and added that she solved such problems seemingly every day optimizing as the paints price and its charging to the containers different capacity[7]

and that she knew this problem very well.

Observing the dance of Olgas fingers on the calculators buttons and the numbers on it display I understood that Olga uses so-called Workers and Peasants and main thing unreliable algorithm of optimization: at first the paint is selected in big tare and then the demand balance (or containers volume) is filled the paint in little tare. This way we pack a suitcase. At first we put massive things to it and then we put to the empty space all small things. Remembered once more Viona (look the footnote) I asked Olga why she did not use the computer and tabular processor Excel for solving these problems. At this moment there was worker page on the display of her computer. On the spot I offered to show how she could it. In Excel there is Solver which dialogue window is called by the command Find the solutionfrom menu Service. In this window user shows the cell keeping criterion function which value we have to maximize, the cells with variables of search (at the beginning of optimization they are empty or keeps the values of first approximation to the maximum) and limitations.