# Linear Problem, need help finding contraints

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• Oct 19th 2008, 12:09 PM
Lindzay0487
Linear Problem, need help finding contraints
The Seaside of Finike is faced with a severe budget shortage. Seeking a long-term solution, the city votes to improve the tax base by replacing an underutilized housing area with a modern development.
The project involves two phases: (1) demolishing substandard houses to provide land for the new development, and (2) building the new development. The following is a summmary of the situation:

• As many as 300 houses can be demolished. Each demolition costs \$2000 and frees up a 0.25 acre lot for development.
• Lot sizes needed for the new single-, double-, and triple-family homes (units) are 0.18, 0.28, and 0.40 acre respectively.
• In the new development the single-family units should be at least 20% of the total. The ratio of triple-family units to double-family units should be at most 1 to 2.
• The construction cost per unit for single, double and triple units is \$50,000, \$70,000, and \$130,000 respectively. Financing through a local bank can amount to a maximum of \$15 million.
• The units are assumed to have a lifetime of 20 years. The NPV of tax levied per unit for single, double, and triple units is \$1000, \$1900, and \$2700, respectively.
The Decision Variables I came up with are:
x1= single units
x2= double units
x3= triple units

The objective function I came up with is:
1000x1+1900x2+2700x3

and the contraints I got so far:
• 2x3-1x2<=0
• .80x1-.20x2-.20x3>=0
• x1+x2+x3<=\$15,000,000
I'm not sure if my answers so far are right, and I am missing contraints. Can anyone let me know if my answers so far are right and what other contraints I need to add?