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by: Ms. Hipolito Willms


Ms. Hipolito Willms
Texas A&M
GPA 3.56


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Class Notes
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This 7 page Class Notes was uploaded by Ms. Hipolito Willms on Wednesday October 21, 2015. The Class Notes belongs to ISEN 420 at Texas A&M University taught by Staff in Fall. Since its upload, it has received 31 views. For similar materials see /class/226199/isen-420-texas-a-m-university in Industrial Engineering at Texas A&M University.

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Date Created: 10/21/15
ISEN 420 Fall 2012 Homework 1 Solutions Section 31 l max Z 30x1 l00x2 st X1 XZS7 Land Constraint 4x1 le2S4O Labor Constraint le1 230 Govt Constraint x120 x220 4 x1 Number of Type l Trucks produced daily xz Number of Type 2 Trucks produced daily Expressing profit in hundreds of dollars we obtain the following formulation max Z 3OOX1 SOOXZ st xlBOO X27OO S l Paint Shop Const xllSOO XZlZOO S l Engine Shop Const X120 X220 Section 34 2 Let x1 Number of valves ordered each month from supplier l xz Number of valves ordered each month from supplier 2 X3 Number of valves ordered each month from supplier 3 Then a correct formulation is min Z 5x1 4xz 3X3 st 4x1 3X2 ZX32500 Receive enough large valves 4x1 35xz 2X32300 Receive enough medium valves 2x1 35x2 6Ox32300 Receive enough small valves X1S7OO 293700 X3S7OO X120 X220 X320 Section 35 3 Let X1 Number of employees who start work on Sunday and work 5 days X2 Number of employees who start work on Monday and work 5 days X7 Number of employees who start work on Saturday and work 5 days Also let ol Number of employees who start work on Sunday and work 6 days 07 Number of employees who start work on Saturday and work 6 days Then the appropriate LP is min 2 250X1X2X7 3l2ol02o7 st X1X4X5X6X7olo3o4o5o6o7le Sunday X1X2X5X6X7ol02o4o5o6o72l7 Monday X1X2X3X6X7ol02o3o5o6o72l3 Tuesday X1X2X3X4X7ol02o3o4o6o72l5 Wednesday X1X2X3X4X5ol02o3o4o5o72l9 Thursday X2X3X4X5X6ol02o3o4o5o62l4 Friday X3X4X5X6X702o3o4o5o6o72l6 Saturday All variables nonnegative Section 3 8 9 Let Xi amount invested in bond iwe assume entire 1000000 will be invested since all investments are always pro table maXz 113X1108X2 112X3 114X4 st 06X1 08X2 10X3 09X4Z08X1 X2 X3 X4 X1S4X1 X2 X3 X4 X2S4X1 X2 X3 X4 X3S4X1 X2 X3 X4 X4S4X1 X2 X3 X4 X1 X2 X3 X4 S 1000000 3X1 4X2 7X3 9X4S6X1 X2 X3 X4 X1 X2 X3 X420 Section 3 9 6 Let P1 hours of process 1 and P2 hours of process 2 Also de ne Xij ounces of chemical i used in drug j Then a correct formulation is maX z 6X11 X21 4X12 X22 st 3P1 2P2S100 Raw Mat 2P1 3P2S120 Labor X11 X12S3P1 3P2 X21 X22S3P1 P2 35X1165X2120 45X12 55X2220 All variables nonnegative ISEN 420 Fall 2012 Homework 2 Solutions Section 31 2 From homework l we see that the LP problem is max Z 30X1 lOOxZ st X1 XZS7 Land Constraint 4x1 leZS4OLabor Constraint le1 230Govt Constraint X120 X220 2a No government constraint is violated 2b No Labor constraint is not satisfied 2c No XZZO is not satisfied 2d Yes all constraints and sign restrictions are satisfied Section 32 l EF is 4x1 leZ 40 CD is x1 3 and AB is X1 xz 7 The feasible region is bounded by ACGH The dotted line in graph is isoprofit line 30x1 l00x2 l20 Point G is optimal At G the constraints l0x1230 and 4x1 leZS4O are binding Thus optimal solution has x1 3 x2 28 and Z 303 l0028 370 A F 4 6 8 10 m Section 3 3 lo Lct x1 dollars bought by paying francs and x2 francs bought by paying dollars Then We wish to solve max 2 x1 7 25x2 st x1 7 25x220 dollar constraint rsxl x220 franc constraint x1 x220 the graph the LP39S fsasibls rsgion s s wssn hs lines indicate by ssgmsnts AB and AC soprofit lines are parallel to AB We inc ass 2 by moving down and to right since AB has larger slops than AC We will have a bounded in 39s i to the inconsistency in the exchange rats i t s FrancsrUsA market of course such an inco t cy in the c rr rkst ld x1 Section 3 10 5 min Z Let Ti Si CI TI i c rs n inveh ory at the end of month i ucks n in entory he end of month l 4005 60052 150TIl 11 TIZ C12 c1 00 c1 7 oo c12 7 c11 c2 7 300 TIl 7 100 T1 7 400 c1 Tlglooo 7 300 c2 nglooo 511500 szlt1500 c1 Tll6 or 4C1 c2 T2Zl6 or 4C2 ALL VARIABLES ZO 6T lZO 6T220 Section 312 2 Let JANl Number of computers rented at beginning of JAN for one nwnth etc Also define lJAN Number of computers available to meet January demand etc The appropriate LP is min Z 200JANl FEBl MARl APRl MAYl JUNEl 350JAN2 FEBZ MAR2 APR2 MAY2JUN2450JAN3FEB3MAR3APR3MAY3JUN3l OMAY33OOJUN3 l75JUN2 st IJAN JANl JAN2 JAN3 IFEB JAN2 JAN3 FEBl FEB2 FEB3 IMAR JAN3 FEB2 FEB3 MARl MAR2 MAR3 IAPR FEB3 MARZ MAR3 APRl APRZ APR3 IMAY MAR3 APR2 APR3 MAYl MAY2 MAY3 IJUN APR3 MAY2 MAY3 JUNl JUN2 JUN3 IJAN29 IFEB25 IMAR27 IAPR29 IMAYZlO IJUNZS All variables 20


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