Email address / usernameMost users should sign in with their email address. If you originally registered with a username please use that to sign in. Sign in via your Institution To purchase short term access, please sign in to your Oxford Academic account above. Simultaneous Equations and Linear Programming -There is a lot of hidden treasure lying within university pages scattered across the internet. This list is an attempt to bring to light those awesome courses which make their high-quality material i.e. assignments, lectures, notes, readings & examinations available online for free. Sign up or log in to customize your list. Here's how it works: Anybody can ask a question The best answers are voted up and rise to the top How to edit a linear programming as the following: Max z = x1 + 12x2 s.t. 3x1 + x2 + 12x3 ≤ 5 x1 + x3 ≤ 16 15x1 + x2 = 14 xj ≥ 0, j=1,2,3. I want the format to be strictly like the example.
Thanks for all the answers below. What I need is just like the picture as following A regular array would suffice here, since the alignment is pretty rigid horizontally: \text{Max} \quad z=x_1 &{} + 12x_2 \\[\jot] \text{s.t.}\qquad 3x_1 &{} + \phantom{12}x_2 &{} + 12x_3 &{} \leq 5 \ x_1 & &{} + \phantom{12}x_3 &{} \leq 16 \ 15x_1 &{} + \phantom{12}x_2 & &{} = 14 \ \multicolumn{4}{c}{x_j \geq 0, \quad j=1,2,3.} The use of \phantom is to allow for proper spacing and alignment. Here might be another alignment option, mainly for the first column: \text{Max} & z=x_1 &{} + 12x_2 \\[\jot] \text{s.t.}& \phantom{15}\llap{3}x_1 &{} + \phantom{12}x_2 &{} + 12x_3 &{} \leq 5 \ & \phantom{15}x_1 & &{} + \phantom{12}x_3 &{} \leq 16 \ & 15x_1 &{} + \phantom{12}x_2 & &{} = 14 \ & \multicolumn{4}{l}{x_j \geq 0, \quad j=1,2,3.} Basically you have a text column, then repeated (math) columns where first one is right-aligned, then a relation column, then left aligned, and again relation column.
Except the last line isn't aligned at all, and the width of the first line shouldn't be taken into account with the alignment of subsequent lines. One way to do this is: \halign{\hfil#\hfil\enspace&& $\hfil\DS#$& ${}#{}$& $\DS{}#\hfil$& ${}#{}$\crcr Max & z = x_1 & + & 12x_2 \hidewidth\cr s.t.& 3x_1 & + & x_2 & + & 12x_3 & \leq & 5 \cr & x_1 & & & + & x_3 & \leq & 16 \cr & 15x_1 & + & x_2 & & & = & 14 \cr oalign{\smallskip $\DS x_j \geq 0, \quad j=1,2,3$.} But please note that this is plain TeX way; it should work with LaTeX as well (sans the \bye at the end), but is generally shunned upon. amsmath provides the alignat* environment. I assume Max and s.t. are not variables, therefore I've typeset them in upright shape. Lonely and empty {} are providing the right amount of spacing. The macro \plus is just a shortcut for +{}. \text{Max} \quad & \mathrlap{z = x_1 + 12 x_2} & & & & & & & & \ \boxSizeOfMax{s.t.} \quad & & 13 x_1 & \plus & x_2 & \plus & 12x_3 & \leq{} & 5 & \ & & x_1 & & & \plus & x_3 & \leq & 16 & \ & & 15 x_1 & \plus & x_2 & & & = & 14 & \ & \mathrlap{x_J\geq 0, j = 1, 2, 3.} & & & & & & & &
You can use \begin{matrix} \end{matrix} too. Here's how your example will be typeset: Maximize $z=x_1 + 12 x_2$ such that \phantom{15}x_1 + &x_2&+&12x_3 &\leqslant 5 & \ \phantom{15}x_1 \phantom{+} & &+&\phantom{12}x_3 &\leqslant 16& \ 15x_1 + &x_2& & &= 14& \ & & & &x_j &\geqslant 0 & j=1,2,3. This time, I tried using alignat* as Peter Grill suggested below: &x_1&{}+{}&x_2&{}+{}&12&&x_3 &&\leqslant 5 & \ &x_1& & &{}+{}& && &&\leqslant 16 & \ 15&x_1&{}+{}&x_2& & && &&=14 & \ & & & & & &&x_3 &&\geqslant0 &\quad j=1,2,3. Attempt 3 :(Just fitting in Peter Grill's suggestions) \text{Max}\quad\rlap{$z = x_1 + 12x_2$} \\ \text{s.t.}\quad&13&x_1&{}+{}&x_2&{}+{}&12&&x_3 &&\;\leqslant &\;5 \\ & &x_1& & &{}+{}& &&x_3 &&\;\leqslant &\;16 \ &15&x_1&{}+{}&x_2& & && &&\; = &\;14 \ & \rlap{$x_j \geqslant 0,\; j=1,2,3.$} Thanks Peter for the suggestion. The output now looks much better. Sign up or log in Sign up using Google Sign up using Email and Password
Post as a guest By posting your answer, you agree to the privacy policy and terms of service. Not the answer you're looking for? Browse other questions tagged math-mode horizontal-alignment or ask your own question. move up Tom Davenports’ analytics maturity curve, they encounter new challenges in using the insights from data analysis and optimisation models. Today, the majority of organisations use descriptive analytics to create insights on what has happened. Also the use of diagnostic analytics to understand why things have happened is becoming more common. Moving up the curve towards predictive and prescriptive analytics is more difficult and requires the development of more advanced analytical capabilities. indicate that about 13% of the companies are using predictivePredictive Analytics provides these companies the capability to identify future probabilities and trends. It will also support the discovery of relations in data not readily apparent with traditional analysis.
insights can be used to for example estimate future demand, which in turn supports sourcing and production decisions. Predictive analytics enables organisations to balance the decisions of today against the conditions that they face in theit allows them to become proactive instead of reactive. these insights into robust decisions is however not always as straight forward scenarios the company wonders how this variability in demand will impact its sourcing with the various demand scenarios? The use of predictive analytics has created more insight, but also increased the complexity of the sourcing and productionTo find out what is best, the company decides to perform a sensitivity analysis on demand using the LP model with the deterministic demand scenario. The analysis shows that although the number of desks and tables produced in each demand scenario differs, no chairs will be produced in any of theGiven this observation, the company decides to go for expected demand
scenario, also a common way of dealing with multiple scenarios in practice. impact of this decision becomes apparent when we look at the profit for each of the demand scenarios based on this decision. Expected profit for sure is notIn the low demand scenario there is a significant loss instead of a small profit, in the most likely scenario there is a slightly lower profit while in the high demand scenario the upward potential doesn’tSo on average the company will be worse off than expected (wheredid we here that before?). The sensitivity analysis on demand didn’t provide any clue that this could happen, it is therefore flawed. Stein Wallace indicates that key to better deal with uncertainty in this case is to have a more thoughtful approach to creating the math model. is inspired by an article of Stein Wallace on sensitivity analysis in linear programming which was published in Interfaces. If you want to experiment yourself a download of an Excel workbook is available.