信息与计算科学-市场调查问题的讨论论文

市场调查问题的讨论摘要 本文关于市场调查问题的讨论，调查消费者对某种新产品的了解和反应情况，根据公司所给出的约束条件求出调查费用的最优解情况，以及在处理实际问题中相关数据变化对最优解的影响。根据题目所给出的条件：共调查 500 个家庭，有、无孩子的家庭个至少各调查 200 个，问卷式调查的家庭至少 300 个，调查有、无孩子的家庭至少各有 50%、60%的问卷式调查，有、无孩子的家庭问卷式调查费用为 50、40，口头调查各为 30、25。将各个方式调查家庭的数量设为决策变量，由此线性规划模型可以得到明确目标函数和约束条件，利用 lingo 软件可得出最优值为 18500。在实际操作中，相关数据改变可能影响最优解。若调查家庭的费用，数量和比例发生变化，通过 lingo 灵敏度分析得出当其在一定的增减区间范围内变化时，对偶价格不变。可以通过对偶价格得到最优解。而这些因子变化超出其合适的增减区间，则需要重新建模求解。最后补充了多个数据同时变化对最优解的影响，若调查家庭的费用和数量在其允许的增减量范围内发生变化且满足百分之一百法则，则对应的最优解和对偶价格不变。如果不满足百分之一百法则，只要其同比例增加或减少，最优解也可能不发生变化。关键词 市场调查 线性规划模型 最优解Discussion on Market ResearchAbstract In this paper, we discuss the problem of market survey, investigate the consumer's understanding and response to a new product, find out the optimal solution of survey cost according to the constraints given by the company, and the impact of relevant data changes on the optimal solution in dealing with practical problems. According to the conditions given by the title: a total of 500 families were investigated, at least 200 families with and without children were investigated respectively, at least 300 families with questionnaire survey, at least 50% and 60% of families with and without children were investigated respectively, the cost of family questionnaire survey with and without children was 50,40, and the cost of oral survey was 30,25 respectively. By setting the number of...