< >诚心求教，是两个公司依靠现有资源争夺客户的问题，最后需要mathematica作图，解题需要的常数参数可以假设...</P>
< >请高手帮忙或者提供解题思路或是有帮助的资料阅读。</P>
< >小弟毫无思路，先谢过了！</P>
<P > </P>
<P >TROLLY WARS<p></p></P>
<P ><p> </p></P>
<P >The Yummy Food Company carried out market research in Trumpton where there was no supermarket and concluded that, were a supermarket to be opened there, it would have access to a lucrative customer base. The company therefore decided to open a supermarket there and launched it with an initial advertising campaign.<p></p></P>
<P ><p> </p></P>
<P >Yummy Food Supermarkets have lower prices than local shops and provide the shopper with a pleasant shopping experience. Therefore having used the supermarket once shoppers always return. In order to attract new customers the supermarket spends, each day, a fixed percentage of its daily revenue on advertising and special offers. The rate of increase of the supermarket’s daily revenue is therefore proportional to the daily revenue that it has already attracted.<p></p></P>
<P ><p> </p></P>
<P >Each potential customer who has not yet visited the supermarket is exposed to this advertising. The rate of increase of the supermarket’s daily revenue is therefore also proportional to the untapped daily revenue remaining in the customer base.<p></p></P>
<P ><p> </p></P>
<P >(1) Use this information to construct a differential equation model which describes how the supermarket’s daily revenue changes in time. Explain your reasoning carefully. (15%)<p></p></P>
<P >(2) Email your model leader. You will then be provided with suitable values to assign to the constants which appear in your model.<p></p></P>
<P >(3) Obtain an analytical solution to your equation and interpret this solution. (15%)<p></p></P>
<P >
<P ><p></p></P><p> </p></P>
<P >Nothing Yummy Food’s success, a rival company called Tasty Nosh decides to open one of its own supermarkets in Trumpton with an initial advertising campaign. Both companied compete for the same pool of untapped daily revenue. Tasty Nosh’s supermarket follows the same advertising policy as Yummy Food’s but with a different measure of effectiveness.<p></p></P>
<P ><p> </p></P>
<P >As well as attracting new daily revenue from the pool of untapped daily revenue each supermarket’s advertising caused some of the other supermarket’s customers to switch their allegiance. The effectiveness of each supermarket in poaching customers from its rival is different.<p></p></P>
<P ><p> </p></P>
<P >(4) Extend the model developed in (1) to describe the competition between the two supermarkets. (20%)<p></p></P>
<P >(5) Email your model leader. You will then be provided with suitable values to assign to the constants which appear in your model.<p></p></P>
<P >(6) Investigate the solution of your model. (20%)<p></p></P>
<P >(7) Discuss ways in which your model might be refined or extended. (30%)<p></p></P>
发表于 2005-7-16 19:34:40
>诚心求教，是两个公司依靠现有资源争夺客户的问题，最后需要mathematica作图，解题需要的常数参数可以假设...</P>