Problem: Article: To calculate marginal cost, you need to know the total cost to produce one unit of whatever product or service you sell. Fixed costs should stay the same throughout your cost analysis, so you need to find the output level at which you would have to increase those fixed expenses. For example, if you own a cupcake bakery, your ovens are a fixed expense. If your ovens are capable of baking 1,000 cupcakes a day, then 1,000 would be the maximum quantity of cupcakes you would consider for your marginal cost analysis. If you produced more than 1,000 cupcakes, your fixed costs would change because you would have to buy an additional oven. You may want to calculate the marginal cost for each individual unit of the product or service you sell. However, this is generally only helpful if you produce relatively few products or services in a day. Otherwise, you probably want to look at the change in quantity as a factor of 10, 50, or even 100.  For example, suppose you run a spa that gives between 3 and 5 massages a day. You want to know the marginal cost of scheduling one additional massage. In this case, it makes sense for your interval to be one.  If you produce products, you may want to look at larger changes in quantity. For example, if your company produces 500 widgets a day, you might want to consider the marginal cost of producing 100 more, then 200 more, and so on. Each interval constitutes a production run. To find the change in quantity, you simply subtract the old quantity from the new quantity. For example, if your company produces 500 widgets a day and you want to look at the marginal cost of producing 600 widgets a day, your change in quantity would be 100.
Summary: Find the output level at which your fixed costs would change. Decide what interval you want to evaluate. Deduct the number of units in the first production run from the number of units in the second production run.

INPUT ARTICLE: Article: Black always goes first in Othello, and the less experienced player should take this color. If the players are equal in skill level, then you may flip a coin to see who gets to be black, or allow the player who lost the last game to be black. This is also known as “outflanking” in Othello. A “row” consists of one or more discs that form a line horizontally, vertically, or diagonally. For example, if the opponent has a disc next to 1 of your discs in a vertical row, then place a disc on the open side of their disc in the same row to outflank your opponent’s disc. Once a disc is outflanked, flip it over to the opposite color. This disc now belongs to you as long as it remains flipped on that side. However, the same disc may be turned over again if it is part of a row that is outflanked. For example, if the disc was white before it was outflanked, then turn it to the black side after it is outflanked. Your opponent’s goal is also to place a disc in a spot that outflanks at least 1 of the first player’s discs. If the second player plays the white discs, they would place 1 of their discs at the end of a row. Your opponent should place their white disc so that a black disc is framed by 2 white discs on each side (or vice versa if you are playing white). Then, make sure your opponent flips the outflanked black disks to white. Remember that the row can be horizontal, diagonal or vertical.

SUMMARY: Allow the less experienced player to go first. Place the first disc in a spot that surrounds an opponent’s disc. Flip the outflanked disc to its opposite side. Pass the turn to your opponent to continue playing.

In one sentence, describe what the following article is about: You will be freezing the lemonade in this. Putting the pan in the freezer will make it extra cold by the time you are ready to add the lemonade. The result will be a somewhat smooth—not quite like a slushy, but not quite like a smoothie either. Save the remaining 1 cup (240 milliliters) of water for later. If you'd like, you can also add ¼ teaspoon of lemon zest for extra flavor and texture. Make sure that everything is evenly mixed together and the sugar is dissolved. During this time, the lemonade will start to freeze and turn to slush. Every 30 minutes, open the freezer, and stir the lemonade with a whisk. This will break up any large, icy chunks, and give you a smoother drink in the end. After the 90 minutes are up, take the pan out of the freezer and mix in the remaining cup of water. Give it a taste. If it is too strong, add a little bit more water. If it is too sour, add some more sugar. If it is too sweet, add a little bit more lemon juice. Pulse it on low for 20 seconds, then on high for 20 more seconds. Make sure that there are no large, icy chunks remaining. This makes either 4 small servings, or 2 large servings. For a fancier drink, garnish it with a sprinkle of lemon zest, a slice of lemon, or a mint leaf.
Summary: Place a 9 by 12 inch (22.86 by 30.48 centimeters) baking pan into the freezer 30 minutes before you start making the lemonade. Combine the sugar, lemon juice, and 2 cups (475 milliliters) of water in a pitcher. Pour the lemonade into the pan, and freeze it for 90 minutes, stirring it every half hour. Whisk in the remaining 1 cup (240 milliliters) of water, and give the lemonade a taste. Pour the frozen lemonade into a blender, and blend until smooth. Pour the frozen lemonade into tall glasses, and serve.

In one sentence, describe what the following article is about: The difference in size will leave a portion of the underlying rug exposed, producing a harmonious framing effect. This is probably the simplest way to layer rugs, and one of the most pleasant and effective from a design standpoint.  Top elaborately patterned rugs with neutral colors in rooms in need of a modest infusion of flair.  Make sure the rugs are made to the same basic dimensions. Otherwise, concentric layering can end up looking lopsided. If your goal is to make a given room look a little more relaxed, leaving the rugs slightly askew will help you achieve this. Uneven layers will also allow you to switch things up in areas with overly linear organization and fill oddly-shaped nooks.  For a more effortlessly casual style, drape the rugs in a more or less random manner. You can also offset rugs at regular intervals, keeping the edges and corners lined up, to add depth without making the setup look sloppy. Avoid covering up more than half of a rug with another, or they make look unbalanced. Choose a thin, pliable rug to go on top of another rug in order to minimize trip hazards. An oblong or rectangular rug stretched over a broader covering performs the same function as a traditional table runner, only from below. Position a long, narrow patterned rug in the center of a wider neutral one serving as a base. You can reserve a space for a combination runner under a dining table, inside an alcove or down the middle of a short hallway.  Layered runner rugs tend to look best when they’re the same length but differ in width. Assemble your own custom runner by connecting several smaller rugs. Disrupt the monotony of plain, dull carpeting with an array of attractive rugs. For instance, a bold solid color draped over an intricate woven pattern can lend a much-need jolt of personality to a basic beige carpet. A good rule of thumb is to look for layers that fall at the opposite end of the design spectrum of your base, such as bold or dark colors on top of lighter ones, or vibrant designs that offer a place for the eye to wander above neutral carpets.  As an added bonus, these rugs can be swapped out at any time, giving you a nearly unlimited number of decorating options.  Use a rug a that’s close to the carpeting, but not an exact match, to highlight subtle textural shifts.
Summary:
Place a small rug on top of a larger one to create a frame. Overlap 2 or more rugs for a homey look. Set down a runner for a pop of color or texture. Layer rugs over carpet to break up the space.