数学专业英语－linear programming
.kantorovich,arussianmathematician,andbytjallingc,koopmans,ayaleeconomist,thefollowingisatypicallinearprogrammingproblem:
thenextsectionisdevotedtosuchinequalities.
recallthatthelinearequationlx+my+n=
aninequalitythatisobtainedfromthelinearequationlx+my+n=0byreplacingtheequalitysign“=”byaninequalitysign<(lessthan),≤lessthanorequalto),>greaterthan),or≥(greaterthanorequalto)
generallyspeaking,,calledtheobjectivefunction,subjecttosomelinearconditions,example2maximizethefunctionf(x,y)=5x+7ysubjecttotheconstraints
x≥0y≥0
x+y-7≤0
2x-3y+6≥0
solutionfirstwefindthesetofallpossiblepairs(x,y)ofnumbersthatsatisfyallfourinequalities..forexample,(0,0)isafeasiblesolutionsince(0,0)satisfies the given conditions; so are (1,2) and (4,3).
secondly, we want to pick the feasible solution for which the given function f (x,y) is a maximum or minimum (maximum in this case). such a feasible solution is called an optimal solution.
since the constraints x≥0andy≥0restrictustothefirstquadrant,=0,y=0,x+y-7=0,and2x-3y+6=0,asshowninfig.2.
fig.2.
thenthefunctionfcantakeonanydesiredvalue.(x,y)=5x+:thatis,wemustlocatethatpoint(x,y)inthepolygonalregionoabcatwhichtheexpression5x+7yhasthemaximumpossiblevalue.
withthisinmind,letusconsidertheequation5x+7y=c,fig.3.
considerthepolygonalregionoabcinfig.3..suchasetofpointsinaplaneiscalledaconvexset.
,thepointb(3,4).
theorem(fundamentaltheoremoflinearprogramming)(orminimum)valueatacornerpointoftheset.
vocabulary
约束条件convexset凸集feaseblesolution容许解，可行解cornerpoint偶角点。
optimalsolution最优解******xmethod单纯形法。
notes这里yalestanford是指美国两间著名的私立大学：耶鲁大学和斯坦福大学，这两间大学分别位于康涅狄格州（connecticut）和加里福尼亚州(california)解作“在某些线形条件的限制下”。试比较下面各词组在用法上的异同：
subjectto;underthecondition(s)of;satisfyingthecondition(s).意思为“著名定理”。
与noticeitfollow都是数学中常用的句型，以表达“根据什么，可得什么”这一意思，请参看附录iii。
5.本课多次用到recall,observe,notice,remember等词，用以提醒读者一些已知的事实或定理，读者可从这些例句中体会这些词的用法。请参看附录iii。
exercise
althoughsatisfactoryfortwo-variablelinearprograms,thecorner--variablesituations.,.the******xmethod,devisedbygeorgedantziginthelate1940’s,was,’sand1960’s.
,.2..点(3,4)是两条直线x+y-7=0和2x-3y+6=0的交点。
2.(3,4)是例2的最优解。
3.计算目标函数在偶角点处的值，然后进行比较，求出目标函数的最大值或最小值。
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