This is an exam question I was practising. I have the general understanding of Linear programming, but how would you go about finding the Decision Variables,  Objective function and Constraints for this?  My Opinions: Decision variables:  $M_1$- # of  Model 1 to be produced  $M_2$ and $M_3$ (similar definition to $M_1$)  Objective function: I'd Multiple the Cost to make in house by cost to buy from subcontractor  to get Minimise: $3900M_1+7500M_2+27300M_3$  Constraints:  $3M_1+1.5M_2+2M_3 \geq 0$  $1.25M_1+2.5M_2+0.75M_3 \geq 0$  $M_1,M_2,M_3 \geq 0$  No idea where number order would go? Do I use it in the Constraints and multiply by the Hours?  Now, am I on the right track?
This is an exam question I was practising. I have the general understanding of Linear programming, but how would you go about finding the Decision Variables, Objective function and Constraints for this?  My Opinions: Decision variables: $M_1$- # of Model $1$ to be produced $M_2$ and $M_3$(similar definition as $M_1$)  Objective function: I'd Multiple the Cost to make in house by cost to buy from subtractor  to get Minimise: $3900M_1+7500M_2+27300M_3$  Constraints: $3M_1+1.5M_2+2M_3\ge0$  $1.25M_1+2.5M_2+0.75M_3\ge8500$  $M_1,M_2,M_3\ge 5500$  No idea where number order would go? Do I use it in the Constraints and multiply by the Hours?  Now, am I on the right track?
What characters are valid in a Java class name? What other rules govern Java class names (for instance, Java class names cannot begin with a number)? Derivative of determinant of a matrix I would like to know how to calculate:  $$\frac{d}{dt}\det \big(A_1(t), A_2(t), \ldots, A_n (t) \big).$$ table of contents: adding a vertical space In a table of contents that has been generated with LaTeX's \tableofcontents command, I would like to add a vertical space before a Chapter item in the table of contents. One way that I have in my notes is to use  \addtocontents{toc}{\protect\vspace{10pt}}   at a desired location in the document so that this gets processed by \tableofcontents to include an appropriate vertical space in the table of contents. I have two questions:   Is the above the correct way to get a vertical space in a table of contents? Why is it necessary to use the \protect command here?   Thank you... The volume on my macbook pro has suddenly become greyed out. I haven't installed any updates or made any modifications to the computer, it just suddenly became greyed out after waking the macbook up from sleeping.  I've tried resetting the PRAM, but I don't hear any chime at all when I start up my computer, no matter how long I wait/how many times the computer re-restarts itself.  There also seem to be no internal speakers detected when I go into system preferences. For both input and output the computer detects 0 devices.  Thanks so much in advance for any help!! How to get pixel data from a UIImage (Cocoa Touch) or CGImage (Core Graphics)? Implement MicroController Power Switch and re-use the button for other features This is similar to other questions, but I feel it is different because of the reuse of the "power" button.   I want a "latching" Momentary Power button.  Behavior:   User Pushes momentary button, holds down as long as necessary and the device powers up. Between Power On and Off the same button will be re-used for other functions  When it is held down for 5 +/- seconds the MicroController will turn itself off.    Design Constraints:   Battery provides between 3.7V to 2.9V during it's usable life The Voltage regulator requires Vin +/- 0.3V on the Enable Pin, 3.1V output. MicroController operates at 3.1V MicroController Output Pin High state is 2.7V Max   Debouncing: In this case I'm not concerned about debouncing the switch, if the user doesn't hold it down long enough for the MicroController to set it's Digital Output pin  High the device doesn't power on.  I've worked up the following schematic, which kind of works.    It assumes 3.7V from the battery. Uses an Analog Input for the Power button, which then uses the variation in voltage to determine if the button has been pressed. In the current design the difference is 0.12 V (from 3.4 to 3.52), but the MicroController has a 12 bit ADC so that shouldn't be a problem, in addition I can adjust the sensitivity range of the ADC.   Questions:  What is the difference between reality and the simulator?  Is there a better way?  How can I get a greater voltage difference on the button input? I've tried many different combinations but they increase the voltage range above the 3.6V Input High Maximum specified in the datasheet.  I'm not excited about the "Leakage current" when the uC Controlled Power Pin is Low, any suggestions?   Thank you for any ideas/suggestions/answers. Automatically keep current version of config files when apt-get install Let's disallow moderator nominations from people who've been suspended in the past year Sum of digits of repunits FireFox 66 Quantum disabled all my extensions at midnight! Should I use static_cast or reinterpret_cast when casting a void* to whatever Both static_cast and reinterpret_cast seem to work fine for casting void* to another pointer type. Is there a good reason to favor one over the other? GIS Point or discrete longitude and latitude columns? I see that the Point type is made to store geometric coordinates, however I don't see what problem it is trying to solve, or what advantages it offers over simply using two numerical columns. It's 16 bytes, so is it just an abstraction for two 8 byte floats? Or is it a string containing some kind of geohash that optimizes the performance of certain queries?  Let's say I want to get all the points for a specific viewport on a Leaflet map... with numerical columns representing latitude and longitude, I'd just filter for all the rows that have a latitude number between the N/S bounds and a longitude number between the E/W bounds, easy. I looked into using Point here, but the syntax is cumbersome and it seems to me like unnecessary overhead for development and for database performance... is it? There are  with not having ftp and telnet present in 10.13 now as per Apple's dictate.  Has anyone found a solid way to bring BSD ftp and telnet back to macOS vs using inetutils? UK visa type to attend conference and training in London Can "Mr", "Mrs", etc. be used with a first name? How many possible electromagnetic wavelengths are possible? Disclaimer: Please keep in mind that I am a young highschool student with no background in physics, this research was done in the course of an hour, and my reasoning could very well be wrong.  After a short conversation about color, I did some thinking, and read  The answer claims that there are $\infty^{\infty}$ colors   My first problem is the definition of colors, I'm going to simplify this (although it's not the same thing) as electromagnetic frequencies. This is what I mean when I refer to color in the rest of this question  The problem with $\infty^{\infty}$ colors is that the plank length exists. This causes two problems to arise with $\infty^{\infty}$. If $l_p$ is assumed to exist (as it is), this means the smallest distance in the universe is $l_p$. So, all wavelengths of light can be divided into a set, of the wavelengths produced by objects at $0^{\circ}$ Kelvin to $\infty^{\circ}$ Kelvin. According to this logic, there are simply $\infty$ colors.  Things are complicated further, when you introduce the Plank Temperature ($P_t$). $P_t$ is the theoretical limit temperature of the universe (at least for the purposes of light and color) Because an object hotter than $P_t$ will produce light with wavelengths shorter than $l_p$. This would introduce an upper limit on colors too.  Wouldn't this mean that the total number of possible colors is equal to however many plank lengths difference there is between an electromagnetic wave produced by a 0 degree object and a $l_p$ object? And therefor far less than $\infty$? Does this reasoning make sense at all? How does one find which files are taking up 80% of the space on a Linux webserver? The drive is constantly filling up. You've hunted down all the spare and random files you can. grep'd for coredump files and even removed some of the un-needed backups...  What would be your next move.  The actual server in question has 10GB of website files and the OS shouldn't take any more than 10GB so how do you track down what's filling a 50GB (virtual) drive? Show that antipodal points remain antipodal under any isometry of $S^2$ "The antipodal map of $S^2$ is the isometry $\bar m$ sending each point $P$ to its opposite point $-P$" (from textbook)  Show that antipodal points remain antipodal under any isometry of $S^2$. In other words, for each isometry f of $S^2$, if $P$ and $P'$ are antipodal, then so are $f(P)$ and $f(P')$  I am unsure how I can define the $P$ and $P'$ so that they are opposites of each other in the antipodal map, and am I supposed to apply the traditional isometries (translation, reflection and rotation) to the points? I don't understand this problem. Prove or disprove: if $\sum\limits_{n=0}^∞a_n$ converges and $\lim\limits_{n\to\infty}b_n =0$, then $\sum\limits_{n=0}^{\infty}a_n b_n$ converges. Loading external GeoJSON file into Leaflet map? I would like to load a geoJSON (polygon) file into my leaflet map. I have seen examples where geoJSON is embedded into the javascript code but I can't find any examples showing how it is done with an external file.   &lt;head&gt;     &lt;meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no"&gt;     &lt;link rel="stylesheet" href="http://cdn.leafletjs.com/leaflet-0.5/leaflet.css" /&gt;     &lt;script src="usStates.geojson" type="text/javascript"&gt;&lt;/script&gt;     &lt;style&gt;         html, body, #map {             height: 100%;         }         body {             padding: 0;             margin: 0;         }     &lt;/style&gt; &lt;/head&gt;  &lt;body&gt;     &lt;div id="map" style="height: 100%"&lt;/div&gt;     &lt;script src="http://d3js.org/d3.v2.min.js?2.9.3"&gt;&lt;/script&gt;     &lt;script src="http://cdn.leafletjs.com/leaflet-0.5/leaflet.js"&gt;&lt;/script&gt;      &lt;script type="text/javascript"&gt;       var map = L.map('map').setView([38.57, -94.71], 4);      L.tileLayer('http://{s}.tile.cloudmade.com/9067860284bc491e92d2342cc51d47d9/998/256/{z}/{x}/{y}.png', {attribution: 'Map data &amp;copy; &lt;a href="http://openstreetmap.org"&gt;OpenStreetMap&lt;/a&gt; Imagery © &lt;a href="http://cloudmade.com"&gt;CloudMade&lt;/a&gt;'}).addTo(map);      var featureStyle = {         "color": "#ff7800",         "weight": 5,          "opacity": 0.2     };      L.geoJson(usStates).addTo(map);      &lt;/script&gt;  &lt;/body&gt;