已知某公司生产AB两种产品，其中生产1件A产品需要1个单位的甲资源，3个单位的丙资源；生产1件B产品需要2个单位的乙资源和2个单位的丙资源。已知现有甲乙丙三种资源4个单位、12个单位和18个单位。通过市场预测，可知A产品的单位市场利润为2元，B产品的单位市场利润为5元。该公司获得最大的市场利润应生产A产品（68）件，此时（69）资源仍有剩余。
- A.0
- B.2
- C.4
- D.6
正确答案及解析
正确答案
解析
本题考查的是线性规划。
假设产品A为X件、产品B为Y件，则：
3X＋2X≤18①
X≤4②
2Y≤12③
利润Z＝2X＋5Y
解不等式首先要把不等式变成等式：
3X+2Y＝18④
X＝4⑤
2Y＝12⑥
当X＝2，Y＝6时，Z最大，Z＝2×2＋5×6＝34，甲资源用了2单元，还剩2单元。
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