Formulate as a goal programming problem
Centerville city council is in the process of developing city tax rates. The annual tax base for real estate property is $750 million and for general sales, $80 million. Annual local gas consumption is estimated at 12 million gallons. They have three goals, listed in order of priority:
1. Tax revenues must be at least $25 million to meet the city's financial commitments.
2. Sales tax cannot exceed 25% of all taxes collected.
3. Gasoline tax cannot exceed 8 cents per gallon.
Answer: Let xp = tax rate for property; xs = sales tax rate, and xg = gas tax in cents per gallon.
Min P1d1-, P2d2-, P3d3+
Subject to:
750xp + 80xs + .12xg ≥ 25
80xs ≤ .25(750xp + 80xs + .12xg)
xg ≤ 8
Simplify the second constraint: 187.5xp - 60xs +.03xg ≥ 0.
If this constraint is written as -187.5xp + 60xs -.03xg = 0,
then the objective function should be: Min P1d1-, P2d2+, P3d3+.
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