A real estate manager, Julie, has a home in Orlando. She wants to lease it out to families visiting the area for vacation. Her desire is to develop a mathematical model using your linear programming skills for maximizing her profit, so she wants to decide how much to charge renters for the house lease.

Essentially, Julie wants to set the lease amount to cover her bills, some future maintenance, and make a small monthly profit. She predicts the home will lease for three weeks out of every month. The investment has monthly bills of $5,800, including mortgage, utilities, and management co. fees. The cleaning fee for each rental is $300. In addition, each time the management co. leases the home for Julie, they charge an additional 15% of the rental fee. Julie does not want to include annual tax refunds in her calculations; she plans to use that money for other investments.

Julie wants to put $1000 away, per month, for future repairs. Julie also desires to make $1000 per month profit. The summer season (May 1 September 15) and holidays (15 December 15 January, Spring Break (15 February 15 March), July 4 week, Thanksgiving week) can charge 25% more for each lease.

Questions:

Consider the monthly costs, the revenue, and the profit goals.

Develop the mathematical model that will give the maximum profit based on the variables and constraints discussed. Define the problem in a sentence and then define the Objective Function.

Define all variables.

List the constraints mathematically.

What assumptions are made based on this model?

What is the breakeven point each month assuming no profit or savings each month?

Graph the breakeven point each month assuming no profit or savings each month.