SOLVSAMP

ProductMix Example1:Productmixproblemwithdiminishingprofitmargin. YourcompanymanufacturesTVs,stereosandspeakers,usingacommonpartsinventory ofpowersupplies,speakercones,etc.Partsareinlimitedsupplyandyoumustdetermine themostprofitablemixofproductstobuild.Butyourprofitperunitbuiltdecreaseswith volumebecauseextrapriceincentivesareneededtoloadthedistributionchannel. TVset Stereo Speaker NumbertoBuild-> PartName Inventory No.Used Chassis PictureTube Diminishing SpeakerCone Returns PowerSupply Exponent: Electronics 0.9 Profits: ByProduct $0 $0 $0 Total $0&FPage&PShippingRoutes Example2:TransportationProblem. Minimizethecostsofshippinggoodsfromproductionplantstowarehousesnearmetropolitandemand centers,whilenotexceedingthesupplyavailablefromeachplantandmeetingthedemandfromeach metropolitanarea. Numbertoshipfromplantxtowarehousey(atintersection): Plants: Total SanFran Denver Chicago Dallas NewYork S.Carolina 5 1 1 1 1 1 Tennessee 5 1 1 1 1 1 Arizona 5 1 1 1 1 1 --- --- --- --- --- Totals: 3 3 3 3 3 DemandsbyWhse--> 180 80 200 160 220 Plants: Supply Shippingcostsfromplantxtowarehousey(atintersection): S.Carolina 310 10 8 6 5 4 Tennessee 260 6 5 4 3 6 Arizona 280 3 4 5 5 9 Shipping: $83 $19 $17 $15 $13 $19&FPage&PStaffScheduling Example3:PersonnelschedulingforanAmusementPark. Foremployeesworkingfiveconsecutivedayswithtwodaysoff,findtheschedule whichmeetsdemandfromattendancelevelswhileminimizingpayrollcosts. Sch. Daysoff Employees Sun Mon Tue Wed Thu Fri Sat A Sunday,Monday 4 0 0 1 1 1 1 1 B Monday,Tuesday 4 1 0 0 1 1 1 1 C Tuesday,Wed. 4 1 1 0 0 1 1 1 D Wed.,Thursday 6 1 1 1 0 0 1 1 E Thursday,Friday 6 1 1 1 1 0 0 1 F Friday,Saturday 4 1 1 1 1 1 0 0 G Saturday,Sunday 4 0 1 1 1 1 1 0 ScheduleTotals: 32 24 24 24 22 20 22 24 TotalDemand: 22 17 13 14 15 18 24 Pay/Employee/Day: $40 Payroll/Week: $1,280&APage&PMaximizingIncome Example4:WorkingCapitalManagement. Determinehowtoinvestexcesscashin1-month,3-monthand6-monthCDssoasto maximizeinterestincomewhilemeetingcompanycashrequirements(plussafetymargin). Yield Term PurchaseCDsinmonths: 1-moCDs: 1.0% 1 1,2,3,4,5and6 Interest 3-moCDs: 4.0% 3 1and4 Earned: 6-moCDs: 9.0% 6 1 Total $7,700 Month: Month1 Month2 Month3 Month4 Month5 Month6 End InitCash: $400,000 $205,000 $216,000 $237,000 $158,400 $109,400 $125,400 MaturCDs: 100,000 100,000 110,000 100,000 100,000 120,000 Interest: 1,000 1,000 1,400 1,000 1,000 2,300 1-moCDs: 100,000 100,000 100,000 100,000 100,000 100,000 3-moCDs: 10,000 10,000 6-moCDs: 10,000 CashUses: 75,000 (10,000) (20,000) 80,000 50,000 (15,000) 60,000 EndCash: $205,000 $216,000 $237,000 $158,400 $109,400 $125,400 $187,700 -290000&FPage&PPortfolioofSecurities Example5:Efficientstockportfolio. Findtheweightingsofstocksinanefficientportfoliowhichmaximizestheportfoliorateof returnforagivenlevelofrisk.ThisworksheetusestheSharpesingle-indexmodel;you canalsousetheMarkowitzmethodifyouhavecovariancetermsavailable. Risk-freerate 6.0% Marketvariance 3.0% Marketrate 15.0% Maximumweight 100.0% Beta ResVar Weight *Beta *Var. StockA 0.80 0.04 20.0% 0.160 0.002 StockB 1.00 0.20 20.0% 0.200 0.008 StockC 1.80 0.12 20.0% 0.360 0.005 StockD 2.20 0.40 20.0% 0.440 0.016 T-bills 0.00 0.00 20.0% 0.000 0.000 Total 100.0% 1.160 0.030 Return Variance PortfolioTotals: 16.4% 7.1% MaximizeReturn:A21:A29 MinimizeRisk:D21:D29 0.1644 0.070768 5 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0&FPage&PEngineeringDesign Example6:Valueofaresistorinanelectricalcircuit. Findthevalueofaresistorinanelectricalcircuitwhichwilldissipatethechargeto1 percentofitsoriginalvaluewithinonetwentiethofasecondaftertheswitchisclosed. Switch-> |----- \ --------- ----| q0= 9 volts | \ | q[t]= 0.09 volts | | | t= 0.05 seconds Battery Capacitor(C) Inductor(L) L= 8 henrys | | | C= 0.0001 farads | | | |----- ----|---- Resistor- ----| R= 300 ohms (R) 1/(L*C) 1250 q[t]= 0.253889184 (R/(2*L))^2 351.5625 SQRT(B15-B16) 29.9739470207 COS(T*B17) 0.0720365271 -R*T/(2*L) -0.9375 Q0*EXP(B19) 3.5244506401&FPage&P