1. Optimization Cont.

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

3. 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 x
100 – 2x
( x)(100 – 2x)

4. The Apartment Problem
Rent = x so Charge $1750

5. 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?

6. 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

7. A = Area of Area of

8.
++++
The wire should be cut 5.279” in from the edge