Optimization Cont.

Objective To solve real-life optimization problems TS: Demonstrating Understanding of Concepts

The Apartment Problem A real estate company owns 100 apartments. At $1000 per month, each apartment can be rented. However, for each $50 increase, there will be two additional vacancies. How much should the real estate company charge for rent to maximize its revenues? Rev=(Rent)(# of apartments) Primary Equation 1,150 94 $108,100 1,200 92 $110,400 1,500 80 $120,000 1000 + 50x 100 – 2x (1000 + 50x)(100 – 2x)

The Apartment Problem Rent = 1000+50x so Charge $1750

The Wire-Cutting Problem A wire 12” is cut into two pieces. One piece is to be shaped into a square and the other piece into a circle. Where should the wire be cut to minimize the area enclosed by the square and circle?

The Wire-Cutting Problem A wire 12” is cut into two pieces. One piece is to be shaped into a square and the other piece into a circle. Where should the wire be cut to minimize the area enclosed by the square and circle? 12” 12-x x A = Area of + Area of

A = Area of + Area of

------- ++++ The wire should be cut 5.279” in from the edge