Context:

A real estate investor wants to build a portfolio of residential and commercial real estate in Texas. They want to create a portfolio that maximizes monthly net income from renting the properties and have $$1$ million in cash to invest.

After researching various markets across Texas, they have identified several promising properties in Austin, Dallas, and San Antonio. The initial cash investment and the net monthly income for each property are shown below $($also included in the starter file$).$ The Cash Investment is the total up$-$front cash cost to acquire and prepare the property $($down payment, fees, maintenance, etc.$).$ The Monthly Net Income is the income earned each month after deducting all costs $($mortgage payment, taxes, maintenance, etc.$).$

Table $($may be out of format but you can see labels along the top and corresponding values below $$ out of alignment$)$

City Property Cash Investment Monthly Net Income

Austin House $1$ $$80,000$ $$400$

Austin House $2$ $$125,000$ $$950$

Austin House $3$ $$180,000$ $$1,100$

Austin Store $$200,000$ $$1,200$

Dallas Apartments $$310,000$ $$2,500$

Dallas House $$150,000$ $$500$

Dallas Office Space $$360,000$ $$4,000$

San Antonio Office Space $$250,000$ $$1,500$

San Antonio Condos $$220,000$ $$2,800$

San Antonio Store $$100,000$ $$500$

There are some conditions the portfolio must meet in order to be diversified:

$1.$ The portfolio can have no more than $2$ properties per city

$2.$ The portfolio can only invest in one house

$3.$ There is no fractional ownership, so the portfolio must fully invest in a property or not invest in that property at all

Questions:

$1.$ Which properties should the investor buy to maximize monthly net income?

Group of answer choices

Austin $-$ House $1$

Austin $-$ House $2$

Austin $-$ House $3$

Austin $-$ Store

Dallas $-$ Apartments

Dallas $-$ House

Dallas $-$ Office Space

San Antonio $-$ Office Space

San Antonio $-$ Condos

San Antonio $-$ Store

$2.$ What is the monthly net income for the optimal portfolio?

$3.$ What is the total cash investment required for the optimal portfolio?

The investor is considering adding a requirement that the portfolio invest in at least one property in each city. Add this constraint for the remaining questions that follow.

$4.$ Does the requirement that at least one property be purchased in each city change the original optimal solution you found?

$5.$ What is the monthly net income for the new optimal portfolio?