《運(yùn)籌學(xué)基礎(chǔ)》2005

1、《運(yùn)籌學(xué)基礎(chǔ)》2005學(xué)號(hào)姓名成績(jī)一(10分)已知線性規(guī)劃問(wèn)題12312312max45212310jzxxxxxxxxx???????????????問(wèn)(1)變量能否成基變量如是得到的基解為何是否是基可行解??12xx(2)變量能否成基變量如是得到的基解為何是否是基可行解??13xx二.(12分)從下面的線性規(guī)劃及對(duì)應(yīng)的單純形表可得出()有唯一最優(yōu)解()有無(wú)界解()無(wú)可行解()最優(yōu)解不唯一(A)化標(biāo)準(zhǔn)型為:得單純形表121212212

2、max351050140zxxxxxxxxx???????????????121241225max3510503140izxxxxxxxxxxx??????????????????x1x2x3x4x5x1|1.00000.00000.00000.20002.0000|2.0000x3|0.00000.00001.00000.20001.0000|5.0000x2|0.00001.00000.00000.00001.0000|4.0000

3、zc|0.00000.00000.00000.20001.0000|(B)得第一階段規(guī)劃為:123123123123123max101512539561515250zxxxxxxxxxxxxxxx?????????????????????11223311112213311212222332max..013jzcxcxcxaxaxaxbstaxaxaxbxj?????????????????將它化成標(biāo)準(zhǔn)型后得單純形表如下：x1x2x3x4

4、x5x3012112052x11120161352zc040421）.求的值。12123ijijabcij??2）寫(xiě)出原問(wèn)題的對(duì)偶問(wèn)題3）求出對(duì)偶問(wèn)題的最優(yōu)解四.(16分)某廠生產(chǎn)IIIIII三種產(chǎn)品其所需勞動(dòng)力材料等有關(guān)數(shù)據(jù)見(jiàn)下表要求:(1)確定獲利最大的產(chǎn)品生產(chǎn)計(jì)劃(2)產(chǎn)品I的利潤(rùn)在什么范圍內(nèi)變動(dòng)時(shí)上述最優(yōu)計(jì)劃不變(3)如果設(shè)計(jì)一種新產(chǎn)品IV單件勞動(dòng)力消耗為8個(gè)單位材料消耗為2個(gè)單位每件獲利3元問(wèn)該種產(chǎn)品是否值得生產(chǎn)(4)如果勞動(dòng)

5、力數(shù)量不增材料不足時(shí)可以從市場(chǎng)購(gòu)買(mǎi)每單位0.4元問(wèn)該廠要不要購(gòu)進(jìn)原材料擴(kuò)大生產(chǎn)以購(gòu)多少為宜IIIIII可用量(單位)勞動(dòng)力63545材料34530利潤(rùn)(元件)314(已知：x4|6.00003.00005.00001.00000.0000|45.0000x5|3.00004.00005.00000.00001.0000|30.0000zc|3.00001.00004.00000.00000.0000|x1|1.00000.5000561