Question

Using ONLY "MS word "formulation, you are required to create a least cost shipping schedule between markets and plants. The markets are New York, Chicago, Topeka and the plants are Seattle, San Diego. Seattle only have 350 units available of supplies and San Diego only have 600 units. The demand are only in New York, Chicago, Topeka respectively 325, 300, 275 units. The cost to ship between markets and plants and is Seattle to New York is 2.5 Seattle to Chicago is 1.7 Seattle to Topeka is 1.8 San Diego to New York is 2.5 San Diego to Chicago is 1.8 San Diego to Topeka is 1.4

Answer 1

Let Cij be the cost to ship from plant i to market j

Let Xij be the number of units transported from plant i to market j

Objective function =Z=Minimize Total cost = Min i j (Xij * Cij )

where i=1,2 for Seattle and San Diego respectively ;

and j=1,2,3 for New York,Chicago and Topeka respectively.

i.e Z= Min (2.5*X11+1.7*X12+1.8*X13+2.5*X21+1.8*X22+1.4*X23)

s.t

Supply constraints :

X11+X12+X13<=350

X21+X22+X23<=600

Demand constraints :

X11+X21=325

X12+X22=300

X13+X23=275

Xij >= 0 (Non-negativity constraint)