# Picture 3.11. The problem about paint

In Mathcad the report of “ control weighing” you can look at the picture 3.11. Commentaries make clear what takes place in formulas. First of all the function Maximize gave fractional result as we had awaited (look the point 2) –we can take fraction quantity of big drums so little drums are needless. Remembered epigraph and the title of the etude I had to go to excess of the versions. In Mathcad-document are formed two matrixes with name Îb (point 3.2) and St (point 3.3). Their elements (there are 1088 elements, i.e. there are 17 columns and 64 lines) keep values of the volume (Îb) and of the worth (St) of paint depending on the combination of the packing. Then (point 3.4) some elements of the matrix Îb are named zero values if the given combinations of the parking do not suit by the worth. The rest is the sleight hand and no mathematics: in point 3.5 number of the line (variable N_15) and of the column (N_55) are determined of the matrix Îb. There is the element with maximum value on their crossing. The reply (6 little and 15 big drums) surprised Olga unpleasantly. She disappointed me unwittingly for 5 litres of paint and for 139 thousand roubles.

The method of searches the coordinates of maximum point that we can see at the picture 3.11 (the double sum) has the considerable limitation: one maximum element has to be in analyzable matrix (in our case it is matrix Ob). If there are a few elements than the reply will be wrong: **the sums** of the points’ coordinates with the maximum elements will be written to the variables N_15 and N_55. We have observed it in point 2 at the picture 3.9.

So Mathcad has spared me almost 150 thousand roubles. This money is not so great but if you added to them new computer etude, new theme of the lecture and new laboratory work and also the author’s emoluments for this book then the play was worth the candles.

Come back from Tambov to Moscow I analyzed this problem once more on my home computer in a comfortable atmosphere. And there is what I have got.