某公司打算经销一种商品,进价为450元/件,售价500元/件。若进货商品一周内售不完,则每件损失50元。假定根据已往统计资料估计,每周最多销售4件,并且每周需求量分别为0、1、2、3和4件的统计概率与统计概率之间的关系如下表所示。

则公司每周进货 ( ) 件可使利润最高。
- A.1
- B.2
- C.3
- D.4
正确答案及解析
正确答案
解析
(1)根据己知条件,可计算出不同进货量及销量下可能获得的收益结果。

第一行,进货量如果是r件,销售一件只能获得50元:如果市场上可以销售两件,但是由于进货量只有1件,因此收益仍然是50元。第二行,如果进货两件,但是只能销售一件,获得50元,同时因为有一件没有卖出去损失50元,两者相抵,总收益为50-50。如果可以销售两件,可以获得收益100元。依次类推可以得到其他收益值。(2)不同进货量及销量下可能获得的收益结果填好以后,根据决策树计算公式,得到进货量为1时的期望收益:500.1+500.2+500.3+500.4=50。同理得到进货量为2、3、4时的期望值。(3)决策结论:进货3件可获得最高收益110元。
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