Critiquing a City's Budget Allocation Model
A city planner is tasked with allocating a total budget of $10 million between building new parks (measured in acres, p) and repairing roads (measured in miles, r). The goal is to maximize the city's 'livability score,' which is represented by the function L(p, r). The cost to develop one acre of park is $500,000, and the cost to repair one mile of road is $250,000.
The planner formulates the problem as follows:
- Maximize: 500,000p + 250,000r
- Subject to the constraint: L(p, r) = 10,000,000
Analyze this formulation. Identify the fundamental error(s) in how the problem has been set up. Explain what the objective function and the constraint should be in this scenario, and write out the correct mathematical formulation of the problem.
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