江西财经大学 2004~2005学年第一学期期末考试试卷 试卷代码:03275A卷 课时:80 课程名称:运筹学Ⅱ(英) 适用对象:管理科学专业 1. Fill in the blanks (10 points) (a)If the objective value is maximum sales revenue, then in dynamic programming, the basic equation is (b) The dynamic programming is divided into two types, they are and (c) The integer programming is divided into three types, they are and The expected queue length is ct (d) For M/M/l model, the expected number of customers in queueing system The waiting time in system for each individual customer is The waiting time in queue for each individual customer is 2. A company is planning its advertising strategy for next year for its three major products Since the three products are quite different, each advertising effort will focus on a single product. In units of millions of dollars, a total of 6 is available for advertising next year, where the advertising expenditure for each product must be an integer greater than or equal to 1. The vice-president for marketing has established the objective: Determine how much to spend on each product in order to maximize total sales. The following table gives the estimated increase in sales(in appropriate units) for the different advertising expenditures Product Advertising expenditure 2 14 24814 4 15 Use dynamic programming to solve this problem. (15 points) 3. Two manufacturers currently are competing for sales in two different but equally profitable product lines. In both cases the sales volume for manufacturer 2 is three times as large as that for manufacturer 1. Because of a recent technological breakthrough. both manufacturers will be making a major improvement in both products. However, they are uncertain as to what development and marketing strategy to follow If both product improvements are developed simultaneously, either manufacturer can have them ready for sale in 12 months. Another alternative as to have a"crash program to develop only one product first to try to get it marketed ahead of the competition. By manufacturer 2 could have one product ready for sale in 9 months, whereas manufacture 1 would require 10 months(because of previous commitments for its production facilities). For1 江西财经大学 2004～2005 学年第一学期期末考试试卷 试卷代码：03275A 卷 课时：80 课程名称：运筹学Ⅱ（英） 适用对象：管理科学专业 1. Fill in the blanks. (10 points) (a) If the objective value is maximum sales revenue, then in dynamic programming, the basic equation is (b) The dynamic programming is divided into two types, they are: and . (c) The integer programming is divided into three types, they are : and . (d) For M/M/1 model, the expected number of customers in queueing system is The expected queue length is The waiting time in system for each individual customer is The waiting time in queue for each individual customer is 2. A company is planning its advertising strategy for next year for its three major products. Since the three products are quite different, each advertising effort will focus on a single product. In units of millions of dollars, a total of 6 is available for advertising next year, where the advertising expenditure for each product must be an integer greater than or equal to 1. The vice-president for marketing has established the objective: Determine how much to spend on each product in order to maximize total sales. The following table gives the estimated increase in sales (in appropriate units) for the different advertising expenditures: Product Advertising expenditure 1 2 3 1 2 3 4 7 10 14 17 4 8 11 14 6 9 13 15 Use dynamic programming to solve this problem. (15 points) 3. Two manufacturers currently are competing for sales in two different but equally profitable product lines. In both cases the sales volume for manufacturer 2 is three times as large as that for manufacturer 1. Because of a recent technological breakthrough, both manufacturers will be making a major improvement in both products. However, they are uncertain as to what development and marketing strategy to follow. If both product improvements are developed simultaneously, either manufacturer can have them ready for sale in 12 months. Another alternative as to have a “crash program” to develop only one product first to try to get it marketed ahead of the competition. By doing this, manufacturer 2 could have one product ready for sale in 9 months, whereas manufacture 1 would require 10 months (because of previous commitments for its production facilities). For