ISE 204 / IE 252 Homework 2
Due: 15.04.201516:00
Anydetection of copyingorplagiarismwillresult in 0 points.
1-) A truckmusttravelfrom New York to Los Angeles. As shown in Figure 68, a variety of routesareavailable. Thenumberassociatedwitheacharc is thenumber of gallons of fuelrequiredbythetruckto traverse thearc. UseDijkstra’salgorithmtofindtheroutefrom New York to Los Angeles thatusesthe minimum amount of gas.
2-)Before a newproduct can be introduced, theactivities in Table 40 must be completed (alltimesare in weeks).
aDraw theprojectdiagram.
bDetermineallcriticalpathsandcriticalactivities.
cDeterminethe total floatforeachactivity.
dSet up an LP that can be usedtodeterminethecriticalpath.
F It is now 12 weeksbeforeChristmas. What is theprobabilitythattheproductwill be in thestoresbeforeChristmas?
gTheduration of eachactivity can be reducedbyupto 2 weeks at thefollowingcostperweek: A, $80; B, $60; C, $30; D, $60; E, $40; F, $30; G, $20. Assumingthattheduration of eachactivity is knownwithcertainty, formulate an LP thatwill minimize thecost of gettingtheproductintothestoresbyChristmas.
3-)StateUniversity has threeprofessorswhoeachteachfourcoursesperyear. Eachyear, foursections of marketing, finance, andproductionmust be offered. At leastonesection of eachclassmust be offeredduringeachsemester (fallandspring). Eachprofessor’s time preferenceandpreferenceforteachingvariouscoursesaregiven in Table 44. The total satisfaction a professorearnsteaching a class is thesum of thesemestersatisfactionandthecoursesatisfaction. Thus, professor 1 derives a satisfaction of 3+6=9 fromteachingmarketingduringthefallsemester. Formulate an MCNFP that can be usedtoassignprofessorstocoursesso as tomaximizethe total satisfaction of thethreeprofessors.
4-)Eastinghousesellsairconditioners. Theannualdemandforairconditioners in eachregion of thecountry is as follows: East, 100,000; South, 150,000; Midwest, 110,000; West, 90,000. Eastinghouseis consideringbuildingtheairconditioners in fourdifferentcities: New York, Atlanta, Chicago, and Los Angeles. Thecost of producing an airconditioner in a cityandshipping it to a region of thecountry is given in Table 18. Anyfactory can produce as many as 150,000 airconditionersperyear. Theannualfixedcost of operating a factory in eachcity is given in Table 19. At least 50,000 units of theMidwestdemandforairconditionersmustcomefrom New York, or at least 50,000 units of theMidwestdemandmustcomefrom Atlanta. Formulate an IP whosesolutionwilltellEastinghouse how to minimize theannualcost of meetingdemandforairconditioners.