Question

1. Dubois Corporation has four outlets across the country: Boston, Dallas, Los Angeles, and St. Paul. Plans call for the following number of products (in 1000s) to be needed at each location.

Boston             70

Dallas              80

Los Angeles    100

St. Paul            100

            Dubois has two warehouses located in St. Louis and Pittsburgh.

Dubois has three plants capable of producing the product. The plants and production capabilities are as follows:

            Denver            100

            Atlanta            100

            Chicago           150

Transportation costs are as follows:

                                    To       St. Louis          Pittsburgh

            From    Denver                  4                      7

                        Atlanta                  5                      4

                        Chicago                 2                      5

                        To                    Boston             Dallas Los Angeles   St. Paul

            From    St. Louis                4                     4                 6               8

                        Pittsburgh              3                     5                 8               7

1. Develop a network representation of this problem.

2. Set up the objective function and the constraints.

Answer 1

Answer:-

Given That:-

Dubois Corporation has four outlets across the country: Boston, Dallas, Los Angeles, and St. Paul. Plans call for the following number of products (in 1000s) to be needed at each location.

The following are the "Transportation costs". is given,

(a)Develop a network representation of this problem.

From	To	St. Louis	Pittsburgh
Denver		4	7
Atlanta		5	4
Chicago		2	5

Decision Variables

* No. of units from each plant to each ware houses are as follows,

From	To	St. Louis	Pittsburgh
Denver		x1	y1
Atlanta		x2	y2
Chicago		x3	y3

* No. of units from each wave house to each location are as follows,

From	To	Boston	Dallas	Los Angeles	St. Paul
St. Louis		4	4	6	8
Pittsburgh		3	5	8	7

From	To	Boston	Dallas	Los Angeles	St. Paul
St. Louis		a1	a2	a3	a4
Pittsburgh		b1	b2	b3	b4

Objective Function

Min Cost:

(b) Set up the objective function and the constraints.

No. of products are as follows

  

Boston	70
Dallas	80
Los Angeles	100
St. Pauls	100

Denver	100
Atlanta	100
Chicago	150

* The above are the abilities of production.

* Therefore, Constraints are as follows

x₁ + y₁ = 100

x₂ + y₂ = 100

x₃ + y₃ = 150

a₁ + b₁ = 70

a₂ + b₂ = 80

a₃ + b₃ = 100

a₄ + b₄ = 100

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