Applied Mathematics for Business and Economics

Lecture Note Linear Programming (LP)

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?

3 A dietician is planning a meal consisting of three foods whose ingredients (per
unit) are summarized in the following table:
Ingredients Food I Food II Food III
Units of protein 5 10 15
Units of carbohydrates 2 3 2
Units of iron 3 6 1
Calories 60 140 120
The dietician wishes to determine the number of units of each food needed to
create a meal containing at least 30 units of protein, 8 units of carbohydrates, and
10 units of iron, with as few calories as possible.
GñkCMnajxagkartmGaharkMBugnwgeRKagerobcMGaharmYyeBlEdlmanmuxmðÚbcMnYn3muxEdleRKOg

pSM¬kñúg1Ékta¦ mandUckñúgtaragxageRkamenH

eRKOgpSM Gahar I Gahar II Gahar III

cMnYnÉktaénRbUetGIun 5 10^15

cMnYnÉktakabUnGIuRdat 2 3 2

cMnYnÉktaénsarCatiEdk 3 6 1

kaLÚrI 60 140 120

GñkCMnajxagkartmGaharenaHcg;kMNt;cMnYnÉktaénmuxmðÚbnImYy²edIm,I[)anGaharmYyeBlEdl

many:agehacCatiRbUetGIun 30 Ékta kabUnGIuRdat 8 Ékta nigCatiEdk 10 Ékta nigkMritkaLÚrI tic

bMputtamEdlGaceFVI)an.

Use graphical technique to solve the given linear programming problems

edayeRbIviFIRkahVic cUredaHRsaycMeNaTkmμviFIlIenEG‘rdUcxageRkam

4 Find the largest and smallest values of Fxy= 5 +

Fxy 5

subject to

cUrrktémøFMbMput nigtUcbMputrbs;GnuKmn_ +

4

= eRkaml½kçx½NÐ

43 2

315

,0

xy

xy

xy

+ ≤

+ ≤

≥

5 Find the smallest value of Fx= 20 + 80 ysubject to: