Rosenberg Land Development $($RLD$)$ is a developer of condominium properties in the Southwest United States. RLD has recently acquired a $40\mathrm{.}625-$acre site outside Phoenix, Arizona. Zoning restrictions allow at most eight units per acre. Three types of condominiums are planned: one$-,$ two$-,$ and three$-$bedroom units. The average construction costs for each type of unit are $$450,000,$ $$600,000,$ and $$750,000,$ respectively. These units will generate a net profit of $10\%.$ The company has equity and loans totaling $$180$ million dollars for this project. From prior development projects, senior managers have determined that there must be a minimum of $15\%$ one$-$bedroom units, $25\%$ two$-$bedroom units, and $25\%$ three$-$bedroom units.

a$.$ Develop a mathematical model to determine how many of each type of unit the developer should build.

b$.$ Implement your model on a spreadsheet and find an optimal solution.