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Note for MATH 1313 with Professor Ahmed-Zaid at UH linear programming

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This 3 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 49 views.

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Date Created: 02/06/15
33 SPKiNQ gull Sec on32 Q yy ll iq39k l Ul Linear Programming A function 5 39 s stem of constraints to be optimized maximized or minimized is called an A system of equalities or inequalities to which an objective function is subject to are called constraints An objective function subject to a system of constraints is called a linear programming problem Example 1 The Soundex Company produces two models of clock radios Each model A 39 s 15 min of on nd 10 min ofwork on Each mo e B re uires 10 min of work on asse 1 line d 12 min of work on assembly line 11 of assembly time 0 an of assembly time on line 11 are 12 available per Soundex s work day It is anticipated that Soundex will realize a pro t of 12 on each model A and 10 on each model B How 1 2 w n 1 G 0 should be produced per day in order t i w i aDef1neyourvariab1es K 39 Lk 6quot WJA ucAfoj O 1 i Y 1 ck Vin3M5 AWE b Construct and 11inatab1e Mag Pt Mu lglk To a mum is M 1Q w ZNOMY E 1393 yaw w 1 E nn No k V Ask L o W 0 95 5 o a NM 11 o c State the Linear Programming Problem Do not solve We ll do this in the next section V V KiW39R 9N9 pi OHQ Vlw l macaw We 4W bKHQK 492 MO HEN Section 32 7 Linear Programming g fj I QfK In 51016 Example 2 A patient in a hospital is required to have s of drug and lIits of drunach day assume that an overdosage of either drug is harmless Two substances M and N contain each of these drugs however in addition both contain an undesirable drug D 3 Each gram of substanc containsunits of drug39units of drug and39units of drug Each gram of substancecontains units of drug quotunits of drug antnunit of drug How manV grams of K 4r 0 SngXoka M Kig i ulf ml H h n n y39 ggww M 9 OE N TOTRLS 7x 35m to lt1 I 9mg 0quot Y g l MM Viv36 Own 03 Miniwi 53 gx39l y wgu o lowly gt39 lx t lt7 km X7gt0 Section 32 7 Linear Programming 2 Example 3 The of cers of a high school senior class are planning to rent buses and vans for a class trip Eacluan transpor students requirwhaperones and costs 1300 to rent Each van can transpo tudents require haperone and cost 0 rent The of cers must plan to accommodate Sinc arents have volunteered to serve as chaperones the of cers must plan to use at most 36 chaperones How many vehicles of each type should the of cers rent in order to minimize the transportation costs What are the minimal transportation costs a De neyourvariables K lk Q Q39 I 1 g DST Vanf b Constructand llinatable i uf l3 w Q Q VOW T01 7K 7 hauls LED 3 D CigarNW 3 IL Min mlkkfbaskC 714100 igloo c State the Linear Programming Pro lem Do not solve We ll do this in the next section Minamm cm L 100gtlt O NLBac YJVD kox igy iii Q 47s JH 3 Kgt0 Section 32 7 Linear Programming 3

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