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    Running a successful business often requires balancing competing needs. If we can model those needs with equations, we can graph them on the same set of axes to compare them. 
    ::经营成功的企业往往需要平衡相互竞争的需求。 如果我们能用方程式来模拟这些需求,我们可以用相同的轴线来比较它们。

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    Break-Even Analysis
    ::平衡分析

    When you first start a business, it is common to have initial costs, like renting a space, buying equipment and materials to produce a product, or paying employees. The business does not start to make any money until you sell enough product to cover these costs, that is, the revenue equals the costs. The point when the revenue finally catches up to the costs is called the break-even point .
    ::当您首次创业时,通常有初始成本,如租用空间、购买生产产品的设备和材料或支付工资的雇员。 企业在销售足够的产品以支付成本之前不会开始赚钱,也就是说,收入等于成本。 收入最终赶上成本的点被称为收支平衡点。

    As you can see in the image above, we can find the break-even point by solving a system of equations. 
    ::正如你在上面的图像中看到的, 我们可以通过解决一个方程式系统 找到平衡点。

    1. Talking Mouths can sell a cell phone for $650 per phone. The fixed costs of the business are $4,550 and the cost per phone is $325. How many phones does the business need to sell to break even?
    ::1. 说话嘴可以卖手机,每部电话650美元,固定业务费用为4 550美元,每部电话费用为325美元。

    2. The Car Dealership buys cars from the manufacturer for $17,000. If the dealership has fixed costs of $32,000 and a cost per car of $50, how many cars must the dealership sell for the sticker price of $25,000 to break even? 
    ::2. 汽车经销商向制造商购买汽车,价格为17 000美元,如果经销商固定费用为32 000美元,每辆车费用为50美元,经销商必须出售多少汽车才能折价出售25 000美元的贴纸?

    Supply and Demand
    ::供应和需求

    As a business, you do not want to have products produced (at your expense) that are sitting on the store shelves and not being bought. You want to make sure the amount of a product that you supply to your store is the same as the amount that customers want to purchase it, or demand it.
    ::作为企业,您不希望生产的产品(由您出钱生产)放在商店货架上而不买。您想确保您向商店供应的产品数量与客户想要购买或要求购买的数量相同。

    The demand especially depends on the price of a product. Let's consider a fancy cell phone. If the cell phone sold for $1, most customers would purchase it. However, if the cell phone sold for $2,500, fewer customers would “demand” it. So, as price goes up, demand goes down.
    ::需求尤其取决于产品的价格。 让我们来考虑一个高档手机。 如果手机以1美元出售,大多数顾客会买。 但是,如果手机以2500美元出售,那么“需求”就会减少。 因此,随着价格的上涨,需求就会下降。

    For supply, as the price of a product goes up, more money goes into the business, so it can supply more product.
    ::就供应而言,随着产品价格上升,更多的钱流入企业,这样它就能提供更多的产品。

    When we graph linear supply and demand curves, we get a graph that looks like this.
    ::当我们绘制线性供求曲线时, 我们得到一个看起来像这个的图表。

    Notice the point where the two models are equal, the equilibrium point, is the solution to a system of equations.
    ::注意两个模型是平等的点,即平衡点,是方程系统的解决办法。

    3. BackSport produces backpacks. If the equation that models the demand is  D = − 10 p + 300  and the equation that models the supply is  S = 15 p + 50 , where p is the price of the backpack, what is the equilibrium point?
    ::3. BackSport产生背包。如果模拟需求方程式是 D10p+300,而模拟供应方程式是 S=15p+50,p是背包的价格,那么平衡点是什么?

    4. Dr. Ray sells headphones. If the equation that models the demand is D = − 4 p + 5000  and the equation that models supply is S = 12 p + 200 , where p is the price of the headphones, what is the equilibrium point? 
    ::4. Ray博士出售耳机:如果模拟需求方程式是D4p+5000,而模型供应方程式是S=12p+200,那么耳机的价格在哪里,平衡点是什么?

    Linear Programming
    ::线线性规划

    As we discussed in the previous connection, linear programming can be used in business applications. Consider the following problem.
    ::正如我们在前一点所讨论的,线性编程可用于商业应用。考虑以下问题。

    5.  In Andrew’s Furniture Shop, he assembles both bookcases and TV cabinets. Each type of furniture takes him about the same time to assemble. He figures he has time to make at most 18 pieces of furniture by this Saturday. The materials for each bookcase cost him $20.00 and the materials for each TV stand cost him $45.00. He has $600.00 to spend on materials. Andrew makes a profit of $60.00 on each bookcase and a profit of $100.00 for each TV stand. Find how many of each piece of furniture Andrew should make so that he maximizes his profit.
    ::5. 在安德鲁家俱店,他组装书架和电视柜子,每类家具都同时让他组装,他估计到本周六他最多有时间做18件家具,每个书架的材料花费他20.00美元,每个电视亭的材料花费他45.00美元,他有600美元用于材料,安德鲁每个书架赚取60.00美元利润,每个电视亭赚取1000.00美元利润,找出每件家具中他应做多少件,以便他最大限度地获得利润。