The city council of Fayetteville is in the process of approving the construction

Question

The city council of Fayetteville is in the process of approving the construction of a new 200,000-ft^2 convention center. Two sites have been proposed, and both require excessing the "eminent domain" law to acquire the property. The following table provides data about proposed (contiguous) properties in both sites together with the acquisition cost.

Site 1:

Property 1, Area (1000 ft^2)=20, Cost ($1000)=1000

Property 2, Area (1000 ft^2)=50, Cost ($1000)=2100

Property 3, Area (1000 ft^2)=50, Cost ($1000)=2350

Property 4, Area (1000 ft^2)=30, Cost ($1000)=1850

Property 5, Area (1000 ft^2)=60, Cost ($1000)=2950

Site 2:

Property 1, Area (1000 ft^2)=80, Cost ($1000)=2800

Property 2, Area (1000 ft^2)=60, Cost ($1000)=1900

Property 3, Area (1000 ft^2)=50, Cost ($1000)=2800

Property 4, Area (1000 ft^2)=70, Cost ($1000)=2500

(Picture of this table attached for further clarification)

Partial acquisition of property is allowed. At least 75% of property 4 must be acquired if site 1 is selected, and at least 50% of property 3 must be acquired if site 2 is selected. Although site 1 property is more expensive (on a per ft^2 basis), the construction cost is less than at site 2, because the infrastructure at site 1 is in much better shape. Construction cost is $25 million at site 1 and $27 million at site 2. Which site should be selected, and what properties should be acquired? Find the solution using excel solver or simplex solver.

Explanation / Answer

Solution using solver in excel:

Total property costs at site 1 = $10.25 million. Construction cost = $25 million. I am assuming the objective is to minimize the total cost. The excel table that i have prepared for site 1 is given below:

The objective will be to minimize the "total cost" cell, subject to the constraints: (1) % acquired of property 4 should be greater than equal to 75% (2) % acquired for all other properties must be greater than equal to 0 (3) sum of all property acquired must be equal to 200 (in 1,000 sq. ft). Solving, we get:

For site 2:

Similar method is used, except the constraint will be that 50% of property 3 is acquired. Solving we get,

Thus, total cost at site 2 is less than site 1, and it should be selected. Property 1 and 2 are acquired fully and property 3 and 4 are acquired 50% each.

Property Area (in 1000 sq. ft) Costs (in 1000 $) % acquired of site total cost (considering the % acquired) area acquired (in 1,000 sq. ft) 1 20 1,000 0 0 2 50 2,100 0 0 3 50 2,350 0 0 4 30 1,850 0 0 5 60 2,950 0 0 Total 0 0 construction cost 25,000 Total cost 25,000

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