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optimization solver with solver with solver

After our first foray to the solver four days ago, we find today's ability to find the solution to an optimization problem.

We have three factories and four warehouses (A, B, C and D). The table in B2: E14 represents unit transport costs of each plant to each warehouse. Line 5 represents the needs of each warehouse and column G which is available at each plant.

The problem to be solved is to find the quantities to be transported (block B9: F11) that will, within the constraints of need and availability, minimize total cost in G14 evaluated by the formula = SUMPRODUCT (B2 : F4, B9: F11) . B12: F12 and G9: G11, finally, we are the vertical and horizontal.

The problem is solved easily by using the solver as we see below with the result, then by setting the solver who has to get it:

Note - Do not you satisfied with the settings above! You must also, before clicking the button "Solve" button
go through the "Options" and check the options " Assume Linear Model "and" Assume Non-negative ".

If you miss the last option, the Excel solver fails to converge! Indeed, he tried in vain to carry negative quantities to reduce the total cost.

If you forget to specify that the model is linear, there will be small rounding errors, and in addition, you will not benefit - after the resolution - all useful information (in particular, the marginal values ).

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Resolution

Let the puzzle mathematical made four days ago. We'll see how today - using the Solver of Excel - you can easily solve this problem, although the algebra is not your forte ...

The model below shows the original formulas in column A, and how we have entered into the model C3: F5. The values of the three variables are in line 2. Formula G3 reproduced until line 5 is: = SUMPRODUCT ($ C $ 2: $ F $ 2, C3: F3) .

Formula G6, finally, is: = SUMPRODUCT (G3: G5 G3: G5) . This formula calculates the sum of squared residuals of the equations: it must result in a score of 0 for the problem to be solved.

We then used the solver of Excel by entering the above parameters. It just click on the button "Solve" for a split second in the final solution with C2, C3 and C4 values 40, 30 and 10.

Note - If you do not see the solver to the right of the tab "Data" is that you must activate it. For this, go through the Office button, click "Excel Options" then "supplements" and then select the solver, go through the button "Go" and finally check and validate the solver ...

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A mathematical puzzle ...

For once, we'll just in this paper to present an algebraic puzzle, as we often see in books of games and mathematical problems. We found this puzzle at the following address: http://www.mathforu.com/sujet-10253.html .

"Jack was twice the age that Yann had when Jack was old Yann. When will
Yann Jack age, they will have between them 90 years.
What ages are they? "

The first part of the first sentence is formulated algebraically in
J = 2 * (Ym) , where the variables represent the age of Jack, one of Yann and a number of years apart .

The second part of the first sentence is a formula even simpler: m = J - Y .

The second sentence can be formulated as follows: J + Y + 2 * (JY) = 90 . It is

not necessary to be a light in algebra to find with these three equations - for three unknowns, thankfully! - The final solution:
J = 40 and Y = 30.

Note 1 - What is interesting is to see how long it took - with the exchange reproduced the above address - before the exact solution is discovered ...

Note 2 - What regulars of this blog may be assured that the link between the enigma and Excel will appear in the next article:)

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Demonstration outside the agricultural show - Sunday, March 7, 2010 (review)

Under a dry cold and windy but the sun pervasive that almost 30 activists have come es denounce the hypocritical image that conveys the agricultural show. The image of animals living in the meadows in the grass under the trees is completely wrong. The vast majority of animals as "livestock" live locked and heaped with the sole focus, the death that awaits them in terror of a slaughterhouse. They are regarded as commodities, as an ordinary consumer product, our company speciesist completely putting aside that like us, animals feel pain, pleasure and did not want to be killed to be turned into steak or chicken leg.
In France, 1 Millard land animals are killed for meat each year, more than 50 billion worldwide. We will not talk about fish, the forever forgotten, because we do not figure.

The objective of this demonstration was to alert the public to denounce the vast deception that is advertising this annual family event. Like every year, many jokes, but despite rejection all, many people stopped to listen to our slogan "Meat = murder", "Ageing: slavery, slaughter: barbarism," "One can live without killing" or "Salon de l'agriculture, outdoor torture" for view our banners, the banner "Antispécistes against the domination of human-es on other animal species," or demand a leaflet. Even more than the slogans chanted at the few texts read megaphone have attracted particular public attention. On the number of visitors who could see us and hear us, we hope that some people finally open their eyes to the dark side this show of lies and cruelty.

Thanks for staying activists es for two hours despite the bad weather.

Photos Guinea_Pig, © Guinea Pig, on http://www.corpsmoderne.net/ ~ guinea-pig / gallery/v/mars2010 / :

Photos by Juliana Marques, http://www.fotolog.com/julianamarques :