###### Explain how quadratic programming is used in the real world.

Write a minimum of 250 words for each of the discussion questions below: A quadratic programming model is an optimization model with n decision variables and m linear constraints, and of the form:

Minimize Z = (1/2) xT Q x + CT x

Subject to: A x ≥ b
x ≥ 0

where x is the n by 1 column vector of decision variables and xT is its transpose, Q is an n by n symmetric matrix of objective parameters, C is an n by 1 vector of additional objective parameters, A is an m by n matrix of constraints parameters, and b is a m by 1 vector of constraints right hand side.

1. Explain how quadratic programming is used in the real world. Provide a specific example from your own line of work, or a line of work that you find particularly interesting. Indicate explicitly and qualitatively what Z, x, Q, C, A, and b are in your example.
2. Harry Markowitz, and Myron Scholes along with Robert Merton are the Nobel Laureates in Economics in 1990 (Markowitz) and 1996 (Scholes and Merton) respectively. Markowitz won the Nobel award for devising his Modern Portfolio Theory (also called: the Markowitz Portfolio Theory – MPT) in 1952. Scholes and Merton were the recipients of Nobel for their Option Pricing and Volatility models introduced in early 1980s. Explain how each of the above two models (MPT and Option Pricing) are related to quadratic programming. Describe the decision variables, the objective function, and the constraints for each model. Tags