Posted: August 1st, 2023

Optimal transportation using Microsoft Solver, accounting homework help

Question description

Consider the following example that demonstrates optimization of transportation.There are production facilities in Battle Creek, Cherry Creek, and Dee Creek with annual capacities of 500 units, 400 units, and 600 units, respectively. The annual demands at warehouses in Worchester, Dorchester, and Rochester are 300 units, 700 units, and 400 units, respectively. The table below gives the unittransportation costs between the production facilities and the warehouses.WorchesterDorchesterRochesterBattle Creek$20/unit$30/unit$13/unitCherry Creek$10/unit$5/unit$17/unitDee Creek$15/unit$12/unit$45/unitHow much ofthe demand at each of the warehouses must be met by each of the production facilities?This problem can be modeled as a linear programming model as follows:Decision VariablesXbw = # of units to be transported from Battle Creek to WorchesterXcw = # of units to be transported from Cherry Creek to WorchesterXdw = # of units to be transported from Dee Creek to WorchesterXbd = # of units to be transported from Battle Creek to DorchesterXcd = # of units to be transported from Cherry Creek to DorchesterXdd = # of units to be transported from Dee Creek to Dorchester2QSO 635 Module SevenXbr = # of units to be transported from Battle Creek to RochesterXcr = # of units to be transported from Cherry Creek to RochesterXdr = # of units to be transported from Dee Creek to RochesterObjective FunctionMinimize total annual transportation cost ($):= 20*Xbw + 10*Xcw + 15*Xdw + 30*Xbd + 5*Xcd + 12*Xdd + 13*Xbr + 17*Xcr + 45*XdrConstraintsDemand ConstraintsXbw + Xcw + Xdw ≥ 300(demand at Worchester)Xbd + Xcd + Xdd ≥ 700(demand at Dorchester)Xbr + Xcr + Xdr ≥ 400(demand at Rochester)Capacity ConstraintsXbw + Xbd + Xbr ≤ 500(capacity at Battle Creek)Xcw + Xcd + Xcr ≤ 400(capacity at Cherry Creek)Xdw + Xdd + Xdr ≤ 600(capacity at Dee Creek)Non-Negativity ConstraintsXbw, Xcw, Xdw, Xbd, Xcd, Xdd, Xbr, Xcr, and Xdr are ≥ 0Integer ConstraintsXbw, Xcw, Xdw, Xbd, Xcd, Xdd, Xbr, Xcr, and Xdr are integers

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