Lecture Note Linear Programming (LP)
48
231
251
xy
xy
xy4
8
+ ≥
+ ≥
+ ≥
Does Fhave a largest value on this feasibility region?
etI FmantémøFMbMput enAelItMbn;EdlGacTTYlyk)anéncemøIyb¤eT cMeBaHlMhat; 6-8?
6 Maximize and minimize the functionFx= 3 +ysubject to the following
constraints
32 0
31
3
,0xy
xy
y
xy8
− ≥
+ ≤
≥
≥
7 Minimize the function Fx=+ 23 ysubject to the following constraints
4
2
319
45 3
32 2
,0
xy
xy
xy
xy+ ≥
+ ≥
+ ≥
≥
8 Minimize the function Fx=+ 3 ysubject to the following constraints
35 38
36
29
,0xy
xy
xy
xy+ ≤
− ≤−
+ ≥
≥
9 At a local leather shop, 1 hour of skilled labor and 1 hour of unskilled labor are
required to produce a briefcase, while 1 hour of skilled labor and 2 hours of
unskilled labor are required to produce a suitcase. The owner of the shop can
make a profit of $15on each briefcase and $20 on each suitcase. On a particular
day, only 7 hours of skilled labor and 11 hours of unskilled labor are available,
and the owner wishes to determine how many briefcases and how many suitcases
to make that day to generate the largest profit possible. enAkñúghagplitniglk;plit
plGMBIEs,kmYy edIm,Iplitv:alIstUcmYyeKRtUvkarkMlaMgBlkmμCMnaj1em:ag nigkMlaMgBlkmμmin
CMnajk¾1em:agEdr. cMeBaHv:alIsFMvijeKRtUvkarkMlaMgBlkmμCMnaj1em:ag nigkMlaMgBlkmμmin
CMnajcMnYn2em:ag. m©as;hag)ancMeNj 15duløaBIv:alIstUcnImYy² nig 20duløaBIv:alIsFMnImYy².
kñúgmYyéf¶NamYyenaH eKGaceRbIkMlaMgBlkmμCMnaj nigminCMnaj)anEt7em:ag nig11em:agerogKña
Etb:ueNÑaH. etIenAkñúgéf¶enaHeKKYrplitniglk;v:alIstUcb:unμan nigFMb:unμanedIm,I[)anR)ak;cMeNj
x<s;bMput?
10 Shipments from one wholesaler contain 3 units of item A, 6 units of item B, 4
units of item C, and cost $20. Shipments from a second wholesaler contain 12
units of item A, 3 units of item B, 3 units of item C, and cost $26. If a retailer
requires at least 396 units of A, 288 units of B and 255 units of C, how many
shipments from each wholesaler should be ordered to minimize total cost?