An office park manager experiments with rental rates and finds that every 1 percent change in per square foot rates induces a 4500 square foot change (in the opposite direction) in the amount of rented space. Rents are currently a $18 per square foot and occupancy is at 90 percent. Fixed operating expenses (those that do not vary with occupancy level) are $7 per square foot; variable operating expenses (assume they vary directly with occupancy level) are $2 per square foot of occupied space. Total space available is 100,000 square feet.

Assuming the relationship between rental rates and occupancy levels remains invariant at all levels, what rental rate will maximum net operating income (revenue minus operating expenses)? Please provide explanation to each step