1/15/18 TALK 1 LINEAR PROGRAMMING Agenda What is Linear - PDF document

1/15/18 TALK 1 LINEAR PROGRAMMING § Agenda • What is Linear Programming? • History • Applications J E S S I C A B E R G A N • Solving WHAT IS LINEAR PROGRAMMING IN OTHER WORDS • Line near P Programmi mming ng i is a a s speciali lized a area o of ma mathe hema matical o l often u n used b by t y the he ____________ a ____________ and nd o othe her v various i ind ndustries t to he help lp t the hem ma m make d decisions ns. . Forma mal De l Defini nition: n: Line near p programmi mming ng i is a a ma mathe hema matical me l metho hod o of • Aids i in a n addressing ng t the he _________ o _________ of ho how t thi hing ngs w work o k or s sho hould ld w work. . _____________________(such a _____________________( h as t the he a allo llocation o n of resources) b by me y means ns o of li line near f func nctions ns w whe here t the he • The he g graphs hs f forme med t thr hrough li h line near p programmi mming ng a als lso a aid i in _____________ d n _____________ data colle llected. . variable les i involv lved a are s subje ject t to c cons nstraint nts. . - M - Merriam- m-Webster Di Dictiona nary y • The o e over erall g goal w when en u using l linea ear p programming i is t to f find t the e ______________________________. ______________________________. EARLY LINEAR PROGRAMMING THE CATALYST The image cannot be displayed. Your _______ provided t _______ p the he s spark, , Starting ng i in t n the he e early 1 ly 18000s computer may The image cannot be displayed. not have urgenc ncy a y and nd f fund nding ng Your computer may not have • _________________, a F _________________, a Frenc nch ma h mathe hema matician a n and nd enough memory enough memory to open the ne needed t to b begin r n research. h. to open the image, or the image may have phys ysicist, f , formu mula lated t the he li line near p programmi mming ng p proble lem. m. image, or the Why? y? been corrupted. Restart your image may have computer, and then open the file again. If the red x still _________________________ _________________________ appears, you may have to _____________. _____________. 1900s 19 delete the image and then insert it again. Ex. L . Large s scale le mi mili litary y • __________________, a __________________, a R Russian ma n mathe hema matician a n and nd pla lanni nning ng f for f fle leets o of econo nomi mist, d , develo loped t the he p proble lem m cargo s shi hips w with s h suppli lies and nd s sold ldiers. . • The he g goal w l was t to i improve ____________ p ____________ pla lanni nning ng i in t n the he US USSR. . 1

1/15/18 IN AMERICA APPLICATIONS 19 1947 – _______________a _______________and nd ______________ ______________ The image cannot be displayed. associates a at t the he U U.S .S. . Your computer may not have enough memory to open the De Departme ment nt o of t the he A Air F Force ______________ ______________ image, or the image may have develo loped t the he been corrupted. Restart your _________________. _________________. ______________ ______________ 1951 – __________________ 19 __________________ ______________ ______________ develo loped a a s special li l line near programmi mming ng s solu lution u n used to p pla lan t n the he o optima mal l ______________ ______________ moveme mo ment nt o of s shi hips b back a k and nd forth a h across t the he A Atla lant ntic during ng t the he w war COMMON GOALS PROBLEM #1 1. 1. ___________ c ___________ cost w whi hile le Dr Dr. . Te Teek, t , the he e emi mine nent nt me medical s l speciali list, c , cla laims ms t tha hat he he c can c n cure c cold lds w with h meeting me ng p product hi his r revolu lutiona nary 3 y 3-la -layer p pills lls. T . The hese c come me i in t n two s sizes: : reg egular s size c cont ntaini ning ng specifications ns 2 g grains ns o of a aspirin, 5 n, 5 g grains ns o of b bicarbona nate, a , and nd 1 1 g grain o n of c codeine ne; ; King s size e 2. 2. ___________ profit w ___________ p with h cont ntaini ning ng 1 1 g grain o n of a aspirin, 8 n, 8 g grains ns o of b bicarbona nate, a , and nd 6 6 g grains ns o of c codeine ne. . optima mal p l production n processes o or p products Now Dr Dr. . Teek’s k’s r research ha h has c convinc nced hi him t m tha hat i it r requires a at le least 1 12 g grains ns of a aspirin, 7 n, 74 g grains ns o of b bicarbona nate, a , and nd 2 28 g grains ns o of c codeine ne t to e effect hi his 3. 3. ____________ c ____________ cost i in n trans nsportation r n routes rema markable le c cure. De . Determi mine ne t the he le least nu numb mber o of p pills lls he he s sho hould ld p prescribe i in n 4. 4. De Determi mine ne b best s sche hedule les order t to me meet t the hese r requireme ment nts. . for p production a n and nd s sale les PROBLEM #1 PROBLEM #1 reg egular s size c cont ntaini ning ng 2 2 g grains ns o of Let x x = = _________ _________ reg egular s size c cont ntaini ning ng 2 2 g grains ns o of x ____a ____and nd y _____ y _____ aspirin, 5 n, 5 g grains ns o of b bicarbona nate, , aspirin, 5 n, 5 g grains ns o of b bicarbona nate, a , and nd _____________ _____________ and nd 1 1 g grain o n of c codeine ne; ; 1 g grain o n of c codeine ne; ; Let y = y = _________ _________ Thi his i is c cons nsidered a a King s size e cont ntaini ning ng 1 1 g grain o n of King s size e cont ntaini ning ng 1 1 g grain o n of a aspirin, 8 n, 8 _____________ _____________ aspirin, 8 n, 8 g grains ns o of b bicarbona nate, , grains ns o of b bicarbona nate, a , and nd 6 6 g grains ns o of ________ ________ o or r restriction. n. and nd 6 6 g grains ns o of c codeine ne. . codeine ne. . Let m = m = ________ ________ Goal: : 12 g grains ns o of a aspirin, 7 n, 74 g grains ns Goal: : 12 g grains ns o of a aspirin, 7 n, 74 g grains ns o of _____________ _____________ of b bicarbona nate, a , and nd 2 28 g grains ns o of bicarbona nate, a , and nd 2 28 g grains ns o of codeine ne codeine ne 2