Q4 (15 points)
The Northside and Southside facilities of Zeron Industries supply three firms (Zrox, Hewes, Rockrite) with customized shelving for its offices. They both order shelving from the same two manufacturers, Arnold Manufacturers and Supershelf, Inc.
Currently weekly demands by the users are 50 for Zrox, 60 for Hewes, and 40 for Rockrite. Both Arnold and Supershelf can supply at most 75 units to its customers.
Because of long standing contracts based on past orders, unit costs from the manufacturers to the suppliers are:
Zeron N Zeron S
Arnold 5 8
Supershelf 7 4
The costs to install the shelving at the various locations are:
Zrox Hewes Rockrite
Thomas 1 5 8
Washburn 3 4 7
The objective is to find the minimum-cost Shipping schedule.
Using all information above, formulate a linear programming model for this problem. Please develop the model in three steps: in the 1st step, identify the Input data, Constraints and Objectives in words clearly; in the 2nd step, define appropriate decision variables (all symbols should have clear meanings) and develop an algebraic model with objective function and all constraints that must be satisfied; in the third step, find the optimal solutions with Excel(solver).
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