b)
B34567891011121314151617181920CDEFGHNPV ($millions)WarehouseFactoryCapital Required($millions)WarehouseFactoryLos Angeles68Los Angeles56San Francisco45San Francisco23San Diego57San Diego34CapitalSpent10<=CapitalAvailable10Build?WarehouseFactoryLos Angeles0<=0San Francisco0<=1San Diego1<=117TotalMaximumWarehousesWarehouses1<=1Total NPV ($millions) 9.8 9.9
See the articles in Interfaces.
a) Let EM = 1 if Eve does the marketing; 0 otherwise
EC = 1 if Eve does the cooking; 0 otherwise ED = 1 if Eve does the dishwashing; 0 otherwise EL = 1 if Eve does the laundry; 0 otherwise SM = 1 if Steven does the marketing; 0 otherwise SC = 1 if Steven does the cooking; 0 otherwise SD = 1 if Steven does the dishwashing; 0 otherwise SL = 1 if Steven does the laundry; 0 otherwise
Minimize Time (hours) = 4.5EM + 7.8EC + 3.6ED + 2.9EL + 4.9SM + 7.2SC + 4.3SD + 3.1SL subject to EM + EC + ED + EL = 2 (each person does 2 tasks) SM + SC + SD + SL = 2 EM + SM = 1 (each task is done by 1 person) EC + SC = 1 ED + SD = 1 EL + SL = 1
and EM, EC, ED, EL, SM, SC, SD, SL are binary variables. b)
A123456789101112BCDEFGH
Time Needed (hours)MarketingEve4.5Steven4.9Does Task?MarketingEve1Steven0Total1=1Cooking7.87.2Dishwashing3.64.3Laundry2.93.1TasksPerformed2=2=Cooking011=1Dishwashing101=1Laundry011=122Total Time (hours)18.4 9-9
9.10
a) Let x1 = 1 if invest in project 1; 0 otherwise x2 = 1 if invest in project 2; 0 otherwise x3 = 1 if invest in project 3; 0 otherwise x4 = 1 if invest in project 4; 0 otherwise x5 = 1 if invest in project 5; 0 otherwise
Maximize NPV ($million) = 1x1 + 1.8x2 + 1.6x3 + 0.8x4 + 1.4x5 subject to 6x1 + 12x2 + 10x3 + 4x4 + 8x5 ≤ 20 ($million capital availa