Building new production and distribution facilities

 

You will need access to Microsoft Excel solver to complete this assignment
here is an additional web location for linear programming for excel
https://www.math.ucla.edu/~tom/LP.pdf
FloridaCorp is a best-in-class manufacturer of widgets and is considering where to build new production and distribution facilities. There are six location options: Daytona, Jacksonville, Miami, Orlando, Tallahassee, and Tampa. The total costs of production and transportation for each possible location pair, the demand for each location, and the costs and production capacity to build each facility are given in the first table from the attached file.
An example to help explain this table is that it costs $90,000 to produce one thousand units in Daytona and transport them to Tampa and $70,000 to produce one thousand units in Daytona and transport to Daytona. For this problem, we assume that these costs are constant and each thousand units cost the same to produce and transport.
In addition to the production and shipping costs, there is a fixed cost to constructing a facility that does not depend on the production volume. There are two possible facility types:
1. Small facility that can produce up to 10 thousand units a year at a fixed cost that depends on the supply region and is given in cells J5:K10
2. Large facility that can produce up to 30 thousand units a year at twice the same fixed cost (thus exhibiting economies of scale since the facility for 200% more fixed costs can make 300% more units). The associated cost and maximum capacity for large facilities are given in cells L5:M10.
Total demand in each region (in thousands of units) is given in cells I5:I10. This demand can be fulfilled from any of the locations, but the CEO has required all demand be filled to ensure customer satisfaction.
As the Vice President of Supply Chain & Logistics for FloridaCorp, you need to decide the following:
1. How many and what type of facilities we should build in each region (note: it will be critical to build enough facilities to meet all demand)
2. How to allocate production between them (example: even if the facility can make 10 units, it might be more cost effective to make only 7 at that particular facility to meet the demand requirements)
3. What locations should each plant supply (example: should a Jacksonville facility service Orlando and Daytona, but not Miami)
Provide an answer to each of these questions by using the attached template. Remember to follow the steps to solve a linear programming problem (hint: you will need to use solver to answer this problem). To help the decision variables, constraints, and objective variable have been structured, but you will have to ensure the formulas to define them are structured correctly, as well as the details in solver including the goal of the objective variable (Hint: it will be key to make sure your decision variables only generate integers) (Final hint: In solver you will have 4 different conditions in the constraint box in Solver).

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